Q: A rectangular loop of wire is placed in a region of uniform magnetic field. If the loop carries a current $$I$$, what is the torque $$\tau$$ experienced by the loop?

$$\tau = \vec{\mu} \times \vec{B}$$

Q: A charged particle moves in a region where both electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ are present. What is the total force $$\vec{F} on $$the particle?

$$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$

Q: A magnetic dipole is placed in a non-uniform magnetic field. What is the net force $$\vec{F} on $$the dipole?

$$\vec{F} = \nabla (\vec{\mu} \cdot \vec{B})$$

Question 1

A proton moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the radius $$r of $$the circular path the proton follows?

Accepted Answer

$$r = \dfrac{mv}{qB}$$

Question 2

Which law is used to calculate the magnetic field at a point due to a current-carrying wire of arbitrary shape?

Accepted Answer

Biot-Savart Law

Question 3

A rectangular loop of wire is placed in a region of uniform magnetic field. If the loop carries a current $$I$$, what is the torque $$	au$$ experienced by the loop?

Accepted Answer

$$	au = \vec{\mu} 	imes \vec{B}$$

Question 4

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

Accepted Answer

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

Question 5

A conducting rod of length $$L$$ moves with velocity $$v$$ perpendicular to a uniform magnetic field $$B. $$What is the motional EMF $$\mathcal{E}$$ induced across the ends of the rod?

Accepted Answer

$$\mathcal{E} = B L v$$

Question 6

Which of the following best describes Lenz's Law?

Accepted Answer

The induced current in a loop always opposes the change in magnetic flux through the loop.

Question 7

A solenoid of length $$l$$ and $$N$$ turns carries a current $$I. $$What is the magnetic field $$B$$ inside the solenoid?

Accepted Answer

$$B = \mu_0$ \dfrac{N}{l} I$$

Question 8

A charged particle moves in a region where both electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ are present. What is the total force $$\vec{F} on $$the particle?

Accepted Answer

$$\vec{F} = q(\vec{E} + \vec{v} 	imes \vec{B})$$

Question 9

Which of the following statements about eddy currents is correct?

Accepted Answer

Eddy currents are loops of electric current induced within conductors by a changing magnetic field.

Question 10

Two parallel wires carry currents $$I_1$$ and $$I_2 in $$the same direction. What is the nature of the force between them?

Accepted Answer

The wires attract each other.

Question 11

A circular loop of radius $$R$$ carries a current $$I. $$What is the magnetic dipole moment $$\mu of $$the loop?

Accepted Answer

$$\mu = I \pi R^2$

Question 12

Which of the following is the correct expression for Faraday's Law of electromagnetic induction?

Accepted Answer

$$\mathcal{E} = -\dfrac{d\Phi_B}{dt}$$

Question 13

A sheet of charge produces a uniform current density $$J. $$Using Ampère’s law, what is the magnetic field $$B$$ just above the sheet?

Accepted Answer

$$B = \dfrac{\mu_0$ J}{2}$$

Question 14

Which type of magnetism is characterized by the alignment of atomic magnetic moments in the same direction, resulting in strong permanent magnets?

Accepted Answer

Ferromagnetism

Question 15

An AC generator rotates a coil in a uniform magnetic field. What is the maximum induced EMF if the coil has $$N$$ turns, area $$A$$, and rotates with angular frequency $$\omega in a $$field $$B$$?

Accepted Answer

$$\mathcal{E}_{max} = N B A \omega$$

Question 16

A charged particle moves in a circle of radius $$r in a $$uniform magnetic field $$B. If $$the particle's speed doubles, what happens to the radius of its path?

Accepted Answer

The radius doubles.

Question 17

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

Accepted Answer

$$F = I L B$$

Question 18

A magnetic dipole is placed in a non-uniform magnetic field. What is the net force $$\vec{F} on $$the dipole?

Accepted Answer

$$\vec{F} = 
abla (\vec{\mu} \cdot \vec{B})$$

Question 19

A resistor of resistance $$R$$ carries a current $$I. $$What is the power loss $$P in $$the resistor?

Accepted Answer

$$P = I^2$ R$$

Study Guide: Magnetic Fields, Forces, and Electromagnetic Induction (Chapters 27–29)

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