# Physics equations/22-Magnetism/Q:AmpereLawCALC/Testbank

## c22Magnetism_ampereLawSymmetry_v1

H is defined by, B=μ0H, where B is magnetic field. A current of 48A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,6.7) to the point (6.7,0).

 a) 9.10E+00 amps b) 9.98E+00 amps c) 1.09E+01 amps d) 1.20E+01 amps e) 1.32E+01 amps

copies
===2===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 52A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.5){{nowrap end}} to the point {{nowrap begin}}(7.5,0){{nowrap end}}.}
-a) 1.19E+01  amps
+b) 1.30E+01  amps
-c) 1.43E+01  amps
-d) 1.56E+01  amps
-e) 1.71E+01  amps
===3===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 78A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,4.6){{nowrap end}} to the point {{nowrap begin}}(4.6,0){{nowrap end}}.}
-a) 1.62E+01  amps
-b) 1.78E+01  amps
+c) 1.95E+01  amps
-d) 2.14E+01  amps
-e) 2.34E+01  amps
===4===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 83A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.4){{nowrap end}} to the point {{nowrap begin}}(7.4,0){{nowrap end}}.}
-a) 1.89E+01  amps
+b) 2.08E+01  amps
-c) 2.28E+01  amps
-d) 2.49E+01  amps
-e) 2.74E+01  amps
===5===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 37A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,8.4){{nowrap end}} to the point {{nowrap begin}}(8.4,0){{nowrap end}}.}
-a) 8.44E+00  amps
+b) 9.25E+00  amps
-c) 1.01E+01  amps
-d) 1.11E+01  amps
-e) 1.22E+01  amps
===6===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 92A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,6.4){{nowrap end}} to the point {{nowrap begin}}(6.4,0){{nowrap end}}.}
-a) 2.10E+01  amps
+b) 2.30E+01  amps
-c) 2.52E+01  amps
-d) 2.77E+01  amps
-e) 3.03E+01  amps
===7===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 87A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9.3){{nowrap end}} to the point {{nowrap begin}}(9.3,0){{nowrap end}}.}
+a) 2.18E+01  amps
-b) 2.38E+01  amps
-c) 2.61E+01  amps
-d) 2.87E+01  amps
-e) 3.14E+01  amps
===8===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 47A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9){{nowrap end}} to the point {{nowrap begin}}(9,0){{nowrap end}}.}
-a) 8.91E+00  amps
-b) 9.77E+00  amps
-c) 1.07E+01  amps
+d) 1.18E+01  amps
-e) 1.29E+01  amps
===9===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 55A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,8.7){{nowrap end}} to the point {{nowrap begin}}(8.7,0){{nowrap end}}.}
+a) 1.38E+01  amps
-b) 1.51E+01  amps
-c) 1.65E+01  amps
-d) 1.81E+01  amps
-e) 1.99E+01  amps
===10===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 92A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.1){{nowrap end}} to the point {{nowrap begin}}(7.1,0){{nowrap end}}.}
+a) 2.30E+01  amps
-b) 2.52E+01  amps
-c) 2.77E+01  amps
-d) 3.03E+01  amps
-e) 3.32E+01  amps
===11===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 40A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,6.7){{nowrap end}} to the point {{nowrap begin}}(6.7,0){{nowrap end}}.}
-a) 8.32E+00  amps
-b) 9.12E+00  amps
+c) 1.00E+01  amps
-d) 1.10E+01  amps
-e) 1.20E+01  amps
===12===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 54A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,5.4){{nowrap end}} to the point {{nowrap begin}}(5.4,0){{nowrap end}}.}
-a) 9.34E+00  amps
-b) 1.02E+01  amps
-c) 1.12E+01  amps
-d) 1.23E+01  amps
+e) 1.35E+01  amps
===13===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 48A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9.3){{nowrap end}} to the point {{nowrap begin}}(9.3,0){{nowrap end}}.}
-a) 9.98E+00  amps
-b) 1.09E+01  amps
+c) 1.20E+01  amps
-d) 1.32E+01  amps
-e) 1.44E+01  amps
===14===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 74A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,4.1){{nowrap end}} to the point {{nowrap begin}}(4.1,0){{nowrap end}}.}
-a) 1.28E+01  amps
-b) 1.40E+01  amps
-c) 1.54E+01  amps
-d) 1.69E+01  amps
+e) 1.85E+01  amps
===15===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 91A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.3){{nowrap end}} to the point {{nowrap begin}}(7.3,0){{nowrap end}}.}
+a) 2.28E+01  amps
-b) 2.49E+01  amps
-c) 2.74E+01  amps
-d) 3.00E+01  amps
-e) 3.29E+01  amps
===16===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 94A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,8.4){{nowrap end}} to the point {{nowrap begin}}(8.4,0){{nowrap end}}.}
-a) 1.63E+01  amps
-b) 1.78E+01  amps
-c) 1.95E+01  amps
-d) 2.14E+01  amps
+e) 2.35E+01  amps
===17===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 63A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,4.6){{nowrap end}} to the point {{nowrap begin}}(4.6,0){{nowrap end}}.}
-a) 1.31E+01  amps
-b) 1.44E+01  amps
+c) 1.58E+01  amps
-d) 1.73E+01  amps
-e) 1.89E+01  amps
===18===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 43A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.1){{nowrap end}} to the point {{nowrap begin}}(7.1,0){{nowrap end}}.}
-a) 8.15E+00  amps
-b) 8.94E+00  amps
-c) 9.80E+00  amps
+d) 1.08E+01  amps
-e) 1.18E+01  amps
===19===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 99A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,6.2){{nowrap end}} to the point {{nowrap begin}}(6.2,0){{nowrap end}}.}
+a) 2.48E+01  amps
-b) 2.71E+01  amps
-c) 2.98E+01  amps
-d) 3.26E+01  amps
-e) 3.58E+01  amps
===20===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 85A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9.8){{nowrap end}} to the point {{nowrap begin}}(9.8,0){{nowrap end}}.}
-a) 1.77E+01  amps
-b) 1.94E+01  amps
+c) 2.13E+01  amps
-d) 2.33E+01  amps
-e) 2.55E+01  amps
===21===
{<!--c22Magnetism_ampereLawSymmetry_1-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 40A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,6.6){{nowrap end}} to the point {{nowrap begin}}(6.6,0){{nowrap end}}.}
+a) 1.00E+01  amps
-b) 1.10E+01  amps
-c) 1.20E+01  amps
-d) 1.32E+01  amps
-e) 1.45E+01  amps


## c22Magnetism_ampereLawSymmetry_v1

H is defined by, B=μ0H, where B is magnetic field. A current of 67A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (-6.1, 6.1) to the point (6.1, 6.1).

 a) 1.27E+01 amps b) 1.39E+01 amps c) 1.53E+01 amps d) 1.68E+01 amps e) 1.84E+01 amps

copies
===2===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 96A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>6.6, 6.6){{nowrap end}} to the point {{nowrap begin}}(6.6, 6.6){{nowrap end}}.}
-a) 1.82E+01  amps
-b) 2.00E+01  amps
-c) 2.19E+01  amps
+d) 2.40E+01  amps
-e) 2.63E+01  amps
===3===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 91A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>9.6, 9.6){{nowrap end}} to the point {{nowrap begin}}(9.6, 9.6){{nowrap end}}.}
-a) 1.73E+01  amps
-b) 1.89E+01  amps
-c) 2.07E+01  amps
+d) 2.28E+01  amps
-e) 2.49E+01  amps
===4===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 74A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>5.7, 5.7){{nowrap end}} to the point {{nowrap begin}}(5.7, 5.7){{nowrap end}}.}
-a) 1.54E+01  amps
-b) 1.69E+01  amps
+c) 1.85E+01  amps
-d) 2.03E+01  amps
-e) 2.22E+01  amps
===5===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 33A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>6.6, 6.6){{nowrap end}} to the point {{nowrap begin}}(6.6, 6.6){{nowrap end}}.}
-a) 5.71E+00  amps
-b) 6.26E+00  amps
-c) 6.86E+00  amps
-d) 7.52E+00  amps
+e) 8.25E+00  amps
===6===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 74A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>7.4, 7.4){{nowrap end}} to the point {{nowrap begin}}(7.4, 7.4){{nowrap end}}.}
-a) 1.69E+01  amps
+b) 1.85E+01  amps
-c) 2.03E+01  amps
-d) 2.22E+01  amps
-e) 2.44E+01  amps
===7===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 96A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>6.4, 6.4){{nowrap end}} to the point {{nowrap begin}}(6.4, 6.4){{nowrap end}}.}
-a) 2.00E+01  amps
-b) 2.19E+01  amps
+c) 2.40E+01  amps
-d) 2.63E+01  amps
-e) 2.89E+01  amps
===8===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 65A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>4.9, 4.9){{nowrap end}} to the point {{nowrap begin}}(4.9, 4.9){{nowrap end}}.}
-a) 1.23E+01  amps
-b) 1.35E+01  amps
-c) 1.48E+01  amps
+d) 1.63E+01  amps
-e) 1.78E+01  amps
===9===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 40A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>9.4, 9.4){{nowrap end}} to the point {{nowrap begin}}(9.4, 9.4){{nowrap end}}.}
-a) 7.59E+00  amps
-b) 8.32E+00  amps
-c) 9.12E+00  amps
+d) 1.00E+01  amps
-e) 1.10E+01  amps
===10===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 77A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>9.8, 9.8){{nowrap end}} to the point {{nowrap begin}}(9.8, 9.8){{nowrap end}}.}
-a) 1.60E+01  amps
-b) 1.76E+01  amps
+c) 1.93E+01  amps
-d) 2.11E+01  amps
-e) 2.31E+01  amps
===11===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 70A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>8.7, 8.7){{nowrap end}} to the point {{nowrap begin}}(8.7, 8.7){{nowrap end}}.}
-a) 1.21E+01  amps
-b) 1.33E+01  amps
-c) 1.46E+01  amps
-d) 1.60E+01  amps
+e) 1.75E+01  amps
===12===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 87A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>6.1, 6.1){{nowrap end}} to the point {{nowrap begin}}(6.1, 6.1){{nowrap end}}.}
-a) 1.50E+01  amps
-b) 1.65E+01  amps
-c) 1.81E+01  amps
-d) 1.98E+01  amps
+e) 2.18E+01  amps
===13===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 94A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>5.8, 5.8){{nowrap end}} to the point {{nowrap begin}}(5.8, 5.8){{nowrap end}}.}
-a) 1.78E+01  amps
-b) 1.95E+01  amps
-c) 2.14E+01  amps
+d) 2.35E+01  amps
-e) 2.58E+01  amps
===14===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 63A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>9.3, 9.3){{nowrap end}} to the point {{nowrap begin}}(9.3, 9.3){{nowrap end}}.}
-a) 1.19E+01  amps
-b) 1.31E+01  amps
-c) 1.44E+01  amps
+d) 1.58E+01  amps
-e) 1.73E+01  amps
===15===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 82A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>9.3, 9.3){{nowrap end}} to the point {{nowrap begin}}(9.3, 9.3){{nowrap end}}.}
+a) 2.05E+01  amps
-b) 2.25E+01  amps
-c) 2.46E+01  amps
-d) 2.70E+01  amps
-e) 2.96E+01  amps
===16===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 51A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>7, 7){{nowrap end}} to the point {{nowrap begin}}(7, 7){{nowrap end}}.}
-a) 9.67E+00  amps
-b) 1.06E+01  amps
-c) 1.16E+01  amps
+d) 1.28E+01  amps
-e) 1.40E+01  amps
===17===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 88A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>8.1, 8.1){{nowrap end}} to the point {{nowrap begin}}(8.1, 8.1){{nowrap end}}.}
-a) 2.01E+01  amps
+b) 2.20E+01  amps
-c) 2.41E+01  amps
-d) 2.64E+01  amps
-e) 2.90E+01  amps
===18===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 51A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>6.8, 6.8){{nowrap end}} to the point {{nowrap begin}}(6.8, 6.8){{nowrap end}}.}
-a) 1.06E+01  amps
-b) 1.16E+01  amps
+c) 1.28E+01  amps
-d) 1.40E+01  amps
-e) 1.53E+01  amps
===19===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 74A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>6.4, 6.4){{nowrap end}} to the point {{nowrap begin}}(6.4, 6.4){{nowrap end}}.}
-a) 1.28E+01  amps
-b) 1.40E+01  amps
-c) 1.54E+01  amps
-d) 1.69E+01  amps
+e) 1.85E+01  amps
===20===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 71A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>8.6, 8.6){{nowrap end}} to the point {{nowrap begin}}(8.6, 8.6){{nowrap end}}.}
-a) 1.62E+01  amps
+b) 1.78E+01  amps
-c) 1.95E+01  amps
-d) 2.13E+01  amps
-e) 2.34E+01  amps
===21===
{<!--c22Magnetism_ampereLawSymmetry_2-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 68A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(<big>-</big>6.4, 6.4){{nowrap end}} to the point {{nowrap begin}}(6.4, 6.4){{nowrap end}}.}
-a) 1.55E+01  amps
+b) 1.70E+01  amps
-c) 1.86E+01  amps
-d) 2.04E+01  amps
-e) 2.24E+01  amps


## c22Magnetism_ampereLawSymmetry_v1

H is defined by, B=μ0H, where B is magnetic field. A current of 84A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from the point (0,9.3) to the point (9.3,9.3).

 a) 1.05E+01 amps b) 1.15E+01 amps c) 1.26E+01 amps d) 1.38E+01 amps e) 1.52E+01 amps

copies
===2===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 33A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9.5){{nowrap end}} to the point {{nowrap begin}}(9.5,9.5){{nowrap end}}.}
-a) 3.43E+00  amps
-b) 3.76E+00  amps
+c) 4.13E+00  amps
-d) 4.52E+00  amps
-e) 4.96E+00  amps
===3===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 37A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9){{nowrap end}} to the point {{nowrap begin}}(9,9){{nowrap end}}.}
-a) 4.22E+00  amps
+b) 4.63E+00  amps
-c) 5.07E+00  amps
-d) 5.56E+00  amps
-e) 6.10E+00  amps
===4===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 88A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,6.6){{nowrap end}} to the point {{nowrap begin}}(6.6,6.6){{nowrap end}}.}
-a) 9.15E+00  amps
-b) 1.00E+01  amps
+c) 1.10E+01  amps
-d) 1.21E+01  amps
-e) 1.32E+01  amps
===5===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 33A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9.8){{nowrap end}} to the point {{nowrap begin}}(9.8,9.8){{nowrap end}}.}
-a) 3.76E+00  amps
+b) 4.13E+00  amps
-c) 4.52E+00  amps
-d) 4.96E+00  amps
-e) 5.44E+00  amps
===6===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 92A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,5.3){{nowrap end}} to the point {{nowrap begin}}(5.3,5.3){{nowrap end}}.}
-a) 8.72E+00  amps
-b) 9.57E+00  amps
-c) 1.05E+01  amps
+d) 1.15E+01  amps
-e) 1.26E+01  amps
===7===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 86A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,5){{nowrap end}} to the point {{nowrap begin}}(5,5){{nowrap end}}.}
-a) 7.44E+00  amps
-b) 8.15E+00  amps
-c) 8.94E+00  amps
-d) 9.80E+00  amps
+e) 1.08E+01  amps
===8===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 46A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.9){{nowrap end}} to the point {{nowrap begin}}(7.9,7.9){{nowrap end}}.}
-a) 5.24E+00  amps
+b) 5.75E+00  amps
-c) 6.30E+00  amps
-d) 6.91E+00  amps
-e) 7.58E+00  amps
===9===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 50A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7){{nowrap end}} to the point {{nowrap begin}}(7,7){{nowrap end}}.}
+a) 6.25E+00  amps
-b) 6.85E+00  amps
-c) 7.51E+00  amps
-d) 8.24E+00  amps
-e) 9.03E+00  amps
===10===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 39A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,8.5){{nowrap end}} to the point {{nowrap begin}}(8.5,8.5){{nowrap end}}.}
+a) 4.88E+00  amps
-b) 5.35E+00  amps
-c) 5.86E+00  amps
-d) 6.43E+00  amps
-e) 7.05E+00  amps
===11===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 59A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.2){{nowrap end}} to the point {{nowrap begin}}(7.2,7.2){{nowrap end}}.}
+a) 7.38E+00  amps
-b) 8.09E+00  amps
-c) 8.87E+00  amps
-d) 9.72E+00  amps
-e) 1.07E+01  amps
===12===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 42A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,4.2){{nowrap end}} to the point {{nowrap begin}}(4.2,4.2){{nowrap end}}.}
-a) 3.98E+00  amps
-b) 4.37E+00  amps
-c) 4.79E+00  amps
+d) 5.25E+00  amps
-e) 5.76E+00  amps
===13===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 36A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,8.6){{nowrap end}} to the point {{nowrap begin}}(8.6,8.6){{nowrap end}}.}
+a) 4.50E+00  amps
-b) 4.93E+00  amps
-c) 5.41E+00  amps
-d) 5.93E+00  amps
-e) 6.50E+00  amps
===14===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 38A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,6.7){{nowrap end}} to the point {{nowrap begin}}(6.7,6.7){{nowrap end}}.}
-a) 4.33E+00  amps
+b) 4.75E+00  amps
-c) 5.21E+00  amps
-d) 5.71E+00  amps
-e) 6.26E+00  amps
===15===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 89A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,4.8){{nowrap end}} to the point {{nowrap begin}}(4.8,4.8){{nowrap end}}.}
-a) 9.25E+00  amps
-b) 1.01E+01  amps
+c) 1.11E+01  amps
-d) 1.22E+01  amps
-e) 1.34E+01  amps
===16===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 48A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,8.4){{nowrap end}} to the point {{nowrap begin}}(8.4,8.4){{nowrap end}}.}
-a) 5.47E+00  amps
+b) 6.00E+00  amps
-c) 6.58E+00  amps
-d) 7.21E+00  amps
-e) 7.91E+00  amps
===17===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 49A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,9.8){{nowrap end}} to the point {{nowrap begin}}(9.8,9.8){{nowrap end}}.}
+a) 6.13E+00  amps
-b) 6.72E+00  amps
-c) 7.36E+00  amps
-d) 8.07E+00  amps
-e) 8.85E+00  amps
===18===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 94A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,5.3){{nowrap end}} to the point {{nowrap begin}}(5.3,5.3){{nowrap end}}.}
-a) 9.77E+00  amps
-b) 1.07E+01  amps
+c) 1.18E+01  amps
-d) 1.29E+01  amps
-e) 1.41E+01  amps
===19===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 31A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.3){{nowrap end}} to the point {{nowrap begin}}(7.3,7.3){{nowrap end}}.}
+a) 3.88E+00  amps
-b) 4.25E+00  amps
-c) 4.66E+00  amps
-d) 5.11E+00  amps
-e) 5.60E+00  amps
===20===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 81A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,7.9){{nowrap end}} to the point {{nowrap begin}}(7.9,7.9){{nowrap end}}.}
-a) 7.68E+00  amps
-b) 8.42E+00  amps
-c) 9.23E+00  amps
+d) 1.01E+01  amps
-e) 1.11E+01  amps
===21===
{<!--c22Magnetism_ampereLawSymmetry_3-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 58A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from the point {{nowrap begin}}(0,8.5){{nowrap end}} to the point {{nowrap begin}}(8.5,8.5){{nowrap end}}.}
-a) 6.03E+00  amps
-b) 6.61E+00  amps
+c) 7.25E+00  amps
-d) 7.95E+00  amps
-e) 8.72E+00  amps


## c22Magnetism_ampereLawSymmetry_v1

H is defined by, B=μ0H, where B is magnetic field. A current of 81A passes along the z-axis. Use symmetry to find the integral, ${\displaystyle \int {\vec {H}}\cdot {\vec {d\ell }}}$, from (-∞,6.4) to (+,6.4).

 a) 3.37E+01 amps b) 3.69E+01 amps c) 4.05E+01 amps d) 4.44E+01 amps e) 4.87E+01 amps

copies
===2===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 94A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,6.2){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,6.2){{nowrap end}}.}
-a) 3.91E+01  amps
-b) 4.29E+01  amps
+c) 4.70E+01  amps
-d) 5.15E+01  amps
-e) 5.65E+01  amps
===3===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 93A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,4.1){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,4.1){{nowrap end}}.}
-a) 3.53E+01  amps
-b) 3.87E+01  amps
-c) 4.24E+01  amps
+d) 4.65E+01  amps
-e) 5.10E+01  amps
===4===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 74A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,9){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,9){{nowrap end}}.}
-a) 3.08E+01  amps
-b) 3.37E+01  amps
+c) 3.70E+01  amps
-d) 4.06E+01  amps
-e) 4.45E+01  amps
===5===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 67A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,9.4){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,9.4){{nowrap end}}.}
-a) 2.32E+01  amps
-b) 2.54E+01  amps
-c) 2.79E+01  amps
-d) 3.06E+01  amps
+e) 3.35E+01  amps
===6===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 31A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,9.2){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,9.2){{nowrap end}}.}
-a) 1.41E+01  amps
+b) 1.55E+01  amps
-c) 1.70E+01  amps
-d) 1.86E+01  amps
-e) 2.04E+01  amps
===7===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 74A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,8.2){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,8.2){{nowrap end}}.}
-a) 3.37E+01  amps
+b) 3.70E+01  amps
-c) 4.06E+01  amps
-d) 4.45E+01  amps
-e) 4.88E+01  amps
===8===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 69A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,5.8){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,5.8){{nowrap end}}.}
-a) 2.87E+01  amps
-b) 3.15E+01  amps
+c) 3.45E+01  amps
-d) 3.78E+01  amps
-e) 4.15E+01  amps
===9===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 85A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,8){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,8){{nowrap end}}.}
-a) 2.94E+01  amps
-b) 3.22E+01  amps
-c) 3.53E+01  amps
-d) 3.88E+01  amps
+e) 4.25E+01  amps
===10===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 88A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,8.7){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,8.7){{nowrap end}}.}
-a) 4.01E+01  amps
+b) 4.40E+01  amps
-c) 4.82E+01  amps
-d) 5.29E+01  amps
-e) 5.80E+01  amps
===11===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 94A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,9.4){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,9.4){{nowrap end}}.}
-a) 3.25E+01  amps
-b) 3.57E+01  amps
-c) 3.91E+01  amps
-d) 4.29E+01  amps
+e) 4.70E+01  amps
===12===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 96A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,8.1){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,8.1){{nowrap end}}.}
-a) 3.32E+01  amps
-b) 3.64E+01  amps
-c) 3.99E+01  amps
-d) 4.38E+01  amps
+e) 4.80E+01  amps
===13===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 36A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,8.3){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,8.3){{nowrap end}}.}
-a) 1.50E+01  amps
-b) 1.64E+01  amps
+c) 1.80E+01  amps
-d) 1.97E+01  amps
-e) 2.16E+01  amps
===14===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 76A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,5.8){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,5.8){{nowrap end}}.}
-a) 3.16E+01  amps
-b) 3.47E+01  amps
+c) 3.80E+01  amps
-d) 4.17E+01  amps
-e) 4.57E+01  amps
===15===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 44A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,5){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,5){{nowrap end}}.}
-a) 1.67E+01  amps
-b) 1.83E+01  amps
-c) 2.01E+01  amps
+d) 2.20E+01  amps
-e) 2.41E+01  amps
===16===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 39A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,8.5){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,8.5){{nowrap end}}.}
-a) 1.62E+01  amps
-b) 1.78E+01  amps
+c) 1.95E+01  amps
-d) 2.14E+01  amps
-e) 2.34E+01  amps
===17===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 43A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,5.8){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,5.8){{nowrap end}}.}
-a) 1.63E+01  amps
-b) 1.79E+01  amps
-c) 1.96E+01  amps
+d) 2.15E+01  amps
-e) 2.36E+01  amps
===18===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 31A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,9.4){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,9.4){{nowrap end}}.}
+a) 1.55E+01  amps
-b) 1.70E+01  amps
-c) 1.86E+01  amps
-d) 2.04E+01  amps
-e) 2.24E+01  amps
===19===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 66A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,5.5){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,5.5){{nowrap end}}.}
-a) 3.01E+01  amps
+b) 3.30E+01  amps
-c) 3.62E+01  amps
-d) 3.97E+01  amps
-e) 4.35E+01  amps
===20===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 76A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,9.6){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,9.6){{nowrap end}}.}
-a) 3.16E+01  amps
-b) 3.47E+01  amps
+c) 3.80E+01  amps
-d) 4.17E+01  amps
-e) 4.57E+01  amps
===21===
{<!--c22Magnetism_ampereLawSymmetry_4-->H is defined by, B=μ<sub>0</sub>H, where B is magnetic field. A current of 67A passes along the z-axis.  Use symmetry to find the integral, $\int \vec H\cdot\vec{d\ell}$, from  {{nowrap begin}}(<big>-∞</big>,6.9){{nowrap end}} to {{nowrap begin}}(+<big>∞</big>,6.9){{nowrap end}}.}
-a) 2.54E+01  amps
-b) 2.79E+01  amps
-c) 3.06E+01  amps
+d) 3.35E+01  amps
-e) 3.67E+01  amps