Q: A 25-cm long wire of mass 8 g carries a 6-A current and is placed in a uniform magnetic field. What magnetic field strength is needed to levitate the wire?

$$B = \frac{mg}{IL} = \frac{(8 \times 10$$^{-3}$$ \ \text{kg})(9.81 \ \text{m/s}^2)}{(6 \ \text{A})(0.25 \ \text{m})} = 0.0052 \ \text{T}$$

Question 1

Which of the following statements about magnetic field lines is correct?

Accepted Answer

Magnetic field lines form continuous, closed loops and never cross each other.

Question 2

A charged particle with charge $$q$$ and velocity $$\vec{v}$$ enters a region with a uniform magnetic field $$\vec{B} at an $$angle $$	heta to $$the field. What is the magnitude of the magnetic force acting on the particle?

Accepted Answer

$$F_B = qvB\sin	heta$$

Question 3

An electron moves in the plane of the screen toward the top. A magnetic field is also in the plane of the screen and directed toward the right. What is the direction of the magnetic force on the electron?

Accepted Answer

Into the screen

Question 4

A proton is moving in a circular orbit of radius $$r in a $$uniform magnetic field $$B$$ perpendicular to its velocity. If the speed of the proton is doubled, what happens to the radius of its circular path?

Accepted Answer

The radius becomes twice as large.

Question 5

A wire carries a current upward in the plane of the screen and experiences a magnetic force toward the right edge of the screen. What is the direction of the magnetic field causing this force?

Accepted Answer

Out of the screen

Question 6

A rectangular loop of wire with area $$A$$ and current $$I is $$placed in a uniform magnetic field $$B. $$The angle between the normal to the loop and the field is $$	heta. $$What is the magnitude of the torque on the loop?

Accepted Answer

$$	au = IAB\sin	heta$$

Question 7

A 25-cm long wire of mass 8 g carries a 6-A current and is placed in a uniform magnetic field. What magnetic field strength is needed to levitate the wire?

Accepted Answer

$$B = \frac{mg}{IL} = \frac{(8 	imes 10$$^{-3}$$ \ 	ext{kg})(9.81 \ 	ext{m/s}^2)}{(6 \ 	ext{A})(0.25 \ 	ext{m})} = 0.0052 \ 	ext{T}$$

Question 8

In a velocity selector, a charged particle moves through perpendicular electric and magnetic fields without deflection. If $$E is $$the electric field and $$B is $$the magnetic field, what is the speed $$v of $$the particle?

Accepted Answer

$$v = \frac{E}{B}$$

Question 9

A rectangular copper strip 1.5 cm wide and 0.10 cm thick carries a current of 5.0 A. A 1.2-T magnetic field is applied perpendicular to the strip. Which of the following best describes the Hall voltage compared to a semiconductor of the same dimensions and current?

Accepted Answer

The Hall voltage is smaller in copper because it has more charge carriers.

Question 10

A charged particle moves in a helical path in a uniform magnetic field. Which component of its velocity remains constant?

Accepted Answer

The component parallel to the magnetic field

Question 11

A mass spectrometer uses a velocity selector and a uniform magnetic field $$B_0 to $$separate ions. If the radius of the ion's path is $$r$$, the electric field in the selector is $$E$$, and the ion's charge is $$q$$, what is the mass-to-charge ratio $$\frac{m}{q}$$?

Accepted Answer

$$\frac{m}{q} = \frac{rB_0B}{E}$$

Question 12

Which of the following best explains why the net magnetic force on a closed current loop in a uniform magnetic field is zero?

Accepted Answer

The forces on opposite sides of the loop are equal in magnitude and opposite in direction.

Question 13

A proton moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the period $$T of $$its circular motion?

Accepted Answer

$$T = \frac{2\pi m}{qB}$$

Question 14

Which of the following is NOT a property of magnetic field lines?

Accepted Answer

They start at the south pole and end at the north pole.

Question 15

A current-carrying wire is placed in a uniform magnetic field. Which equation gives the magnitude of the force on a straight segment of length $$L$$ carrying current $$I at an $$angle $$	heta to $$the field?

Accepted Answer

$$F = ILB\sin	heta$$

Question 16

Which of the following best describes the Hall effect?

Accepted Answer

A potential difference is generated perpendicular to both the current and the magnetic field in a conductor.

Question 17

A rectangular loop with $$N$$ turns, area $$A$$, and current $$I is $$placed in a uniform magnetic field $$B. $$What is the expression for its magnetic dipole moment?

Accepted Answer

$$\mu = NIA$$

Question 18

Which of the following is true about the work done by a magnetic force on a moving charged particle?

Accepted Answer

The magnetic force does no work on the particle.

Magnetic Fields and Forces: Study Notes for Physics College Students

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