Q: A point charge $$q$$ moves with velocity $$\vec{v} as $$shown in the figure. According to the Biot-Savart law, what is the expression for the magnetic field $$\vec{B} at a $$point $$\vec{r}$$ from the charge?

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

Q: Which of the following best describes the Biot-Savart law for the magnetic field $$d\vec{B}$$ due to a current element $$I d\vec{l} at a $$point $$\vec{r}$$?

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

Q: The permeability of free space $$\mu_0$ is:

$$\mu_0$ = 4\pi \times 10$$^{-7}$$\,\mathrm{N/A^2$}$$

Question 1

A point charge $$q$$ moves with velocity $$\vec{v} as $$shown in the figure. According to the Biot-Savart law, what is the expression for the magnetic field $$\vec{B} at a $$point $$\vec{r}$$ from the charge?

Accepted Answer

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

Question 2

Which of the following best describes the Biot-Savart law for the magnetic field $$d\vec{B}$$ due to a current element $$I d\vec{l} at a $$point $$\vec{r}$$?

Accepted Answer

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

Question 3

What is the SI unit of the magnetic field $$\vec{B}$$, and how is it defined in terms of the Ampere?

Accepted Answer

Tesla (T), defined as $$1\,\mathrm{T} = 1\,\mathrm{N}/(\mathrm{A}\cdot\mathrm{m})$$

Question 4

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

Accepted Answer

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

Question 5

Two long, parallel wires carry currents $$I_1$$ and $$I_2 in $$the same direction and are separated by a distance $$r. $$What is the force per unit length between them?

Accepted Answer

$$F/L = \frac{\mu_0$}{2\pi} \frac{I_1$ I_2$}{r}$$

Question 6

If the currents in two parallel wires are in opposite directions, what is the nature of the force between them?

Accepted Answer

The wires repel each other.

Question 7

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

Accepted Answer

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

Question 8

What is the direction of the magnetic field at the center of a current-carrying loop?

Accepted Answer

Perpendicular to the plane of the loop, determined by the right-hand rule.

Question 9

The magnetic dipole moment $$\vec{\mu} of a $$current loop with current $$I$$ and area $$A is $$given by:

Accepted Answer

$$\vec{\mu} = I \vec{A}$$

Question 10

Which of the following statements about the force between two parallel current-carrying wires is correct?

Accepted Answer

The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions.

Question 11

A current $$I$$ flows through a wire segment of length $$L in a $$uniform magnetic field $$B$$ perpendicular to the wire. What is the magnitude of the force on the wire?

Accepted Answer

$$F = I L B$$

Question 12

The permeability of free space $$\mu_0$ is:

Accepted Answer

$$\mu_0$ = 4\pi 	imes 10$$^{-7}$$\,\mathrm{N/A^2$}$$

Question 13

Which law is used to derive the magnetic field due to a moving point charge?

Accepted Answer

The Biot-Savart law

Question 14

For a circular current loop, the magnetic field on the axis at a distance $$x$$ from the center is:

Accepted Answer

$$B = \frac{\mu_0$ I R^2$}{2 (x^2$ + R^2$)^{3/2}$$}$

Question 15

The direction of the magnetic field produced by a current-carrying wire can be determined by:

Accepted Answer

The right-hand rule

Sources of Magnetic Field: Biot-Savart Law, Magnetic Fields from Currents, and Applications

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