Q: Which equation correctly describes the magnetic field $B(r)$ generated at position $r$ by a point charge $q$ moving with constant velocity $v$?

$B(r) = \frac{\mu_0 q v \times \hat{r}}{4 \pi r^2}$

Q: What is the value of the permeability of free space $\mu_0$?

$\mu_0 = 4 \pi \times 10^{-7} \ \mathrm{T \cdot m \cdot A^{-1}}$

Q: Which equation represents the Biot-Savart Law for the magnetic field $dB$ generated by a current element $I d\vec{l}$ at a point $r$?

$dB = \frac{\mu_0 I d\vec{l} \times \hat{r}}{4 \pi r^2}$

Question 1

Which equation correctly describes the magnetic field $B(r)$ generated at position $r$ by a point charge $q$ moving with constant velocity $v$?

Accepted Answer

$B(r) = \frac{\mu_0 q v 	imes \hat{r}}{4 \pi r^2}$

Question 2

A straight wire carries a current $I$. According to the right-hand rule, what is the direction of the magnetic field around the wire?

Accepted Answer

In concentric circles around the wire, direction given by curling the fingers of the right hand with thumb pointing in the direction of current

Question 3

Which law allows you to calculate the magnetic field generated by a current-carrying wire by integrating around a closed loop?

Accepted Answer

Ampere's Law

Question 4

What is the magnetic field at a distance $r$ from an infinitely long straight wire carrying current $I$?

Accepted Answer

$B = \frac{\mu_0 I}{2 \pi r}$

Question 5

Two parallel wires carry currents in the same direction. What is the nature of the force between them?

Accepted Answer

They attract each other

Question 6

A circular loop of radius $a$ carries a current $I$. What is the magnetic field at the center of the loop?

Accepted Answer

$B = \frac{\mu_0 I}{2a}$

Question 7

Which of the following materials is most likely to be diamagnetic?

Accepted Answer

Bismuth

Question 8

What is the torque $	au$ experienced by a magnetic dipole $\mu$ in a uniform magnetic field $B$?

Accepted Answer

$	au = \mu 	imes B$

Question 9

A paramagnetic material is placed in an external magnetic field $B_0$. What happens to the total magnetic field inside the material?

Accepted Answer

It increases compared to $B_0$

Question 10

Which equation describes the force on a moving charge $q$ in both electric and magnetic fields?

Accepted Answer

$F = q(E + v 	imes B)$

Question 11

If two positive point charges move side by side in the same direction with the same velocity, what is the direction of the magnetic force that one exerts on the other?

Accepted Answer

Toward the other charge (attractive)

Question 12

Which of the following is true for the magnetic field generated by a moving charge?

Accepted Answer

It is perpendicular to both the velocity and the position vector from the charge

Question 13

What is the value of the permeability of free space $\mu_0$?

Accepted Answer

$\mu_0 = 4 \pi 	imes 10^{-7} \ \mathrm{T \cdot m \cdot A^{-1}}$

Question 14

Which of the following statements about ferromagnetic materials is correct?

Accepted Answer

Their magnetic domains can spontaneously align even without an external field

Question 15

A rectangular loop carrying current $I$ is placed near a long straight wire also carrying current $I$. What is the net magnetic force on the loop?

Accepted Answer

Zero

Question 16

Which equation represents the Biot-Savart Law for the magnetic field $dB$ generated by a current element $I d\vec{l}$ at a point $r$?

Accepted Answer

$dB = \frac{\mu_0 I d\vec{l} 	imes \hat{r}}{4 \pi r^2}$

Question 17

What is the effect of placing a diamagnetic material in an external magnetic field $B_0$?

Accepted Answer

The total magnetic field inside the material decreases

Question 18

Which of the following best describes the principle of superposition for magnetic fields generated by multiple moving charges?

Accepted Answer

The total magnetic field is the sum of the fields generated by each charge individually

Question 19

Which equation describes the electric field $E(r)$ generated by a point charge $q$ at the origin?

Accepted Answer

$E(r) = \frac{q}{4 \pi \epsilon_0 r^2} \hat{r}$

Sources of Magnetic Field: Moving Charges, Currents, and Magnetic Materials

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