Q: The Biot-Savart law gives the magnetic field $$d\vec{B} at a $$point $$P$$ due to a small segment $$d\vec{\ell} of $$current $$I as$$:

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

Q: A particle with charge $$q$$ moves with velocity $$\vec{v} at a $$distance $$r$$ from point $$P. $$What is the magnetic field at $$P$$ due to this particle?

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

Question 1

Which of the following best describes the fundamental source of all magnetic fields?

Accepted Answer

Electric charges in motion

Question 2

A long straight wire carries a current $$I. $$What is the magnitude of the magnetic field at a distance $$r$$ from the wire?

Accepted Answer

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

Question 3

Which right-hand rule is used to determine the direction of the magnetic dipole moment $$\vec{\mu}$$ for a current loop?

Accepted Answer

Curl your fingers in the direction of the current; your thumb points in the direction of $$\vec{\mu}$$

Question 4

A rectangular current loop is placed in a uniform magnetic field with its plane perpendicular to the field. What does the field exert on the loop?

Accepted Answer

A net torque

Question 5

Which of the following statements about the magnetic field inside a long solenoid carrying a steady current is correct?

Accepted Answer

It is spatially uniform in magnitude

Question 6

Ampère’s law states that the line integral of the magnetic field $$\vec{B}$$ around a closed path is proportional to:

Accepted Answer

The current encircled by the path

Question 7

A toroid has $$N$$ windings and carries a current $$I. $$What is the magnitude of the magnetic field inside the windings at a distance $$r$$ from the center?

Accepted Answer

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

Question 8

Which of the following is true about the line integral of the magnetic field $$\vec{B}$$ along a closed path that does NOT encircle any current-carrying wire?

Accepted Answer

It is zero

Question 9

The Biot-Savart law gives the magnetic field $$d\vec{B} at a $$point $$P$$ due to a small segment $$d\vec{\ell} of $$current $$I as$$:

Accepted Answer

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

Question 10

A particle with charge $$q$$ moves with velocity $$\vec{v} at a $$distance $$r$$ from point $$P. $$What is the magnetic field at $$P$$ due to this particle?

Accepted Answer

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

Question 11

If the current $$I$$ through a long straight wire is doubled, what happens to the magnetic field at a fixed distance $$r$$ from the wire?

Accepted Answer

It is doubled

Question 12

Which of the following best describes the magnetic field outside an infinitely long solenoid?

Accepted Answer

It is zero

Question 13

A current loop is placed in a uniform magnetic field such that its magnetic dipole moment $$\vec{\mu} is $$parallel to $$\vec{B}. $$What torque does it experience?

Accepted Answer

No torque

Question 14

The product of the permeability of free space $$\mu_0$ and the permittivity of free space $$\$$epsilon_0 is $$related to the speed of light $$c_0 by$$:

Accepted Answer

$$\mu_0$ \$$epsilon_0$$ = (c_0$)^{-2}$

Question 15

A large flat sheet carries a current per unit width $$K. $$What is the magnitude of the magnetic field a distance $$d$$ above the sheet?

Accepted Answer

$$B = \frac{\mu_0$ K}{2}$$

Question 16

Which of the following is a correct statement about the interaction of stationary charged particles?

Accepted Answer

They interact only electrically

Question 17

A wire is bent into a circular arc of radius $$R$$ subtending an angle $$\phi$$ and carries a current $$I. $$What is the magnitude of the magnetic field at the center of the arc?

Accepted Answer

$$B = \frac{\mu_0$ I \phi}{4\pi R}$$

Question 18

How does the value of the line integral of the electrostatic field along a closed path encircling a charge distribution compare with the value of the line integral of the magnetic field along a closed path encircling a long straight current-carrying wire?

Accepted Answer

It is zero in the electric case and non-zero in the magnetic case

Magnetic Fields of Charged Particles in Motion: Sources, Laws, and Applications

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