Q: Which of the following correctly expresses the Biot-Savart Law for the magnetic field $$d\mathbf{B}$$ produced at point P by a current element $$I d\mathbf{L}$$?

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

Q: A solenoid is used in an MRI machine to create a uniform magnetic field. If the solenoid has 1000 turns per meter and carries a current of 2 A, what is the magnitude of the magnetic field inside the solenoid?

$$B = \mu_0$ n I = (4\pi \times 10$$^{-7}$$ \ \mathrm{T\cdot m/A}) \times 1000 \times 2 = 2.51 \times 10$$^{-3}$$ \ \mathrm{T}$$

Question 1

Which of the following correctly expresses the Biot-Savart Law for the magnetic field $$d\mathbf{B}$$ produced at point P by a current element $$I d\mathbf{L}$$?

Accepted Answer

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

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

For a circular coil of radius $$R$$ carrying current $$I$$, what is the magnetic field at the center of the coil?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

A solenoid has $$n$$ turns per unit length and carries a current $$I. $$What is the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I$$

Question 6

Using Ampere's Law, what is the magnetic field inside a cylindrical conductor of radius $$R at a $$distance $$r \u003c R$$ from the center, assuming uniform current density?

Accepted Answer

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

Question 7

A wire carries current out of the page. What is the direction of the magnetic field lines around the wire?

Accepted Answer

Counterclockwise, as given by the right-hand rule

Question 8

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

Accepted Answer

They repel each other

Question 9

What is the expression for the magnetic field on the axis of a circular coil of radius $$R at a $$distance $$z$$ from its center?

Accepted Answer

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

Question 10

A wire carries a current $$I$$ into the page. Using Ampere's Law, 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 11

A solenoid is used in an MRI machine to create a uniform magnetic field. If the solenoid has 1000 turns per meter and carries a current of 2 A, what is the magnitude of the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I = (4\pi 	imes 10$$^{-7}$$ \ \mathrm{T\cdot m/A}) 	imes 1000 	imes 2 = 2.51 	imes 10$$^{-3}$$ \ \mathrm{T}$$

Question 12

A circular coil of radius $$R$$ carries a current $$I. At a $$point far along the axis ($$z \gg R$$), what is the approximate expression for the magnetic field?

Accepted Answer

$$B_z \approx \frac{\mu_0$ I R^2$}{2 z^3$}$$

Question 13

Which of the following statements about the right-hand rule for magnetic fields is correct?

Accepted Answer

If you point your thumb in the direction of current, your fingers curl in the direction of the magnetic field lines

Question 14

A cylindrical conductor of radius $$R$$ carries a total current $$I$$ uniformly distributed. What is the magnetic field outside the conductor ($$r \u003e R$$)?

Accepted Answer

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

Question 15

A wire loop encloses three wires carrying currents $$-3I$$, $$+14I$$, and $$-6I ($$currents into the page are negative, out of the page are positive). What is the net current enclosed by the loop?

Accepted Answer

$$+5I ($$out of the page)

Question 16

Which situation is best suited for applying Ampere's Law to find the magnetic field?

Accepted Answer

A long straight wire with cylindrical symmetry

Question 17

Two parallel wires, each of length $$L$$, are separated by distance $$d$$ and carry currents $$I_1$$ and $$I_2 to $$the right. What is the magnitude of the force on wire 2 due to wire 1?

Accepted Answer

$$F_{12} = \frac{\mu_0$ I_1$ I_2$ L}{2\pi d}$$

Question 18

A toroid is a coil shaped like a donut. Which law would you use to calculate the magnetic field inside a toroid?

Accepted Answer

Ampere's Law

Current and Magnetic Fields: Biot-Savart Law, Ampère's Law, and Applications

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