OpenStax University Physics/E&M/Sources of Magnetic Fields

$ℰ\mathrm{\&}ℳ$ (Vol. 2):    5:Electric Charges and Fields    6:Gauss's Law    7:Electric Potential    8:Capacitance    9:Current and Resistance    10:Direct-Current Circuits    11:Magnetic Forces and Fields    12:Sources of Magnetic Fields    13:Electromagnetic Induction    14:Inductance    15:Alternating-Current Circuits    16:Electromagnetic Waves

Subpages

Chapter 12

Sources of Magnetic Fields

▭ Permeability of free space ${\mu }_0=4\pi \times 10^{-7}$ T·m/A
▭ Force between parallel wires $\frac{F}{\ell }=\frac{{\mu }_0{I}_1{I}_2}{2\pi r}$

▭ Biot–Savart law $\overrightarrow{B}=\frac{{\mu }_0}{4\pi }\underset{wire}{\int }\frac{Id\overrightarrow{\ell }\times \hat{r}}{r^2}$

▭ Ampère's Law:$\oint \overrightarrow{B}\cdot d\overrightarrow{\ell }={\mu }_0{I}_{enc}$
▭ Magnetic field due to long straight wire $B=\frac{{\mu }_{0}I}{2\pi R}$ ▭ At center of loop $B=\frac{{\mu }_{0}I}{2R}$
▭ Inside a long thin solenoid $B={\mu }_{0}nI$ where $n=N/\ell$ is the ratio of the number of turns to the solenoid's length.
▭ Inside a toroid $B=\frac{{\mu }_{0}N}{2\pi r}$

▭ The magnetic field inside a solenoid filled with paramagnetic material is $B=\mu nI$ where $\mu =(1+\chi ){\mu }_0$ is the permeability

For quiz at QB/d_cp2.12

Free space permeability ${\mu }_0=4\pi \times 10^{-7}$ T·m/A
Force between parallel wires $\frac{F}{\ell }=\frac{{\mu }_0{I}_1{I}_2}{2\pi r}$
Biot–Savart law $\overrightarrow{B}=\frac{{\mu }_0}{4\pi }\underset{wire}{\int }\frac{Id\overrightarrow{\ell }\times \hat{r}}{r^2}$
Ampère's Law:$\oint \overrightarrow{B}\cdot d\overrightarrow{\ell }=4\pi {\mu }_0{I}_{enc}$
Magnetic field inside solenoid with paramagnetic material =$B=\mu nI$ where $\mu =(1+\chi ){\mu }_0$= permeability