OpenStax University Physics/Archived sample/T1V1

PhysicsCalc2152657831440

PhysicsCalc2:T1:V1

PhysicsCalc2152657831440

1) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
 ${\vec {\mathfrak {F}}}=(2+1.45z)\rho ^{2}{\hat {\rho }}+8.02z^{3}{\hat {z}}$
Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate ,
 $\left|\int _{side}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$
over the curved side surface of the cylinder.

a) 4.021E+02

b) 4.872E+02

c) 5.902E+02

d) 7.151E+02

e) 8.663E+02

2) A 0.5 Farad capacitor charged with 1.6 Coulombs. What is the energy stored in the capacitor if the plates are 0.7 mm apart?

a) 2.23 J.

b) 2.56 J.

c) 2.94 J.

d) 3.39 J.

e) 3.89 J.

3) A proton is accellerated (at rest) from a plate held at 767.8 volts to a plate at zero volts. What is the final speed?

a) 1.1 x 10⁵ m/s.

b) 1.7 x 10⁵ m/s.

c) 2.6 x 10⁵ m/s.

d) 3.8 x 10⁵ m/s.

e) 5.8 x 10⁵ m/s.

4) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?

a) 1826 N.

b) 2099 N.

c) 2414 N.

d) 2776 N.

e) 3193 N.

5) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at (x,y) =( 1.1a, 1.2a) is βkQ/a², where β equals

a) 2.86 x 10^-1 unit

b) 3.47 x 10^-1 unit

c) 4.2 x 10^-1 unit

d) 5.09 x 10^-1 unit

e) 6.17 x 10^-1 unit

6) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {F}}=$:

a) 1/2

b) 2

c) 2/3

d) 3

e) 3/2

7) How fast is a 2663 eV electron moving?

a) 3.1 x 10⁷ m/s.

b) 4.6 x 10⁷ m/s.

c) 6.9 x 10⁷ m/s.

d) 1 x 10⁸ m/s.

e) 1.5 x 10⁸ m/s.

8) Integrate the line integral of ${\vec {F}}=4xy{\hat {x}}+9.8x{\hat {y}}$ from the origin to the point at x = 2.6 and y = 3.9

a) 7.93E+01

b) 8.48E+01

c) 9.08E+01

d) 9.71E+01

e) 1.04E+02

9) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,
 ${\vec {\mathfrak {F}}}=(1.88+1.29z)\rho ^{2}{\hat {\rho }}+7.2z^{2}{\hat {z}}$
Let ${\hat {n}}$ be the outward unit normal to this cylinder and evaluate ,
 $\left|\int _{top}{\vec {\mathfrak {F}}}\cdot {\hat {n}}dA\right|\,$
over the top surface of the cylinder.

a) 1.248E+03

b) 1.512E+03

c) 1.832E+03

d) 2.220E+03

e) 2.689E+03

10) A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) s−4

b) 5−s

c) 5

d) 1−s

e) s−1

11) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at (x,y) =( 5a, 4a) is βkQ/a², where β equals

a) 1.76 x 10^-3 unit

b) 2.13 x 10^-3 unit

c) 2.59 x 10^-3 unit

d) 3.13 x 10^-3 unit

e) 3.79 x 10^-3 unit

12) A line of charge density λ situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
$Answer$ (assuming ${\mathcal {B}}>{\mathcal {A}}$) $is:{\frac {1}{4\pi \epsilon _{0}}}\int _{\mathcal {A}}^{\mathcal {B}}{\frac {{\mathcal {C}}\;\lambda ds}{\left[{\mathcal {D}}^{2}+{\mathcal {E}}^{2}\right]^{\mathcal {F}}\;}}$, where ${\mathcal {C}}=$:

a) 8

b) s−3

c) 3−s

d) s−7

e) 7−s