Q: A rectangular current loop with long side $$l = 18\ \mathrm{cm}$$ and short side $$w = 7.2\ \mathrm{cm}$$ carries a current $$I = 0.5\ \mathrm{A}. $$What is the magnitude of the magnetic dipole moment of the loop?

$$m = I \times l \times w = 0.5 \times 0.18 \times 0.072 = 0.00648\ \mathrm{A\cdot m^2$}$$

Q: An electron moves with velocity $$\vec{v} = 1.5 \times 10^6$\ \mathrm{m/s}$$ through a region with a uniform magnetic field $$\vec{B} = 1.3\ \mathrm{T}. $$What is the magnitude of the Lorentz force acting on the electron?

$$F = |q|vB = 1.6 \times 10$$^{-19}$$ \times 1.5 \times 10^6$ \times 1.3 = 3.12 \times 10$$^{-13}$$\ \mathrm{N}$$

Q: A straight wire of length $$L = 3.3\ \mathrm{m}$$ carries a current $$I = 3.3\ \mathrm{A}$$ and is placed in a uniform magnetic field $$B = 0.43\ \mathrm{T} at an $$angle $$\theta = 45^\circ to $$the field. What is the magnitude of the force on the wire?

$$F = I L B \sin\theta = 3.3 \times 3.3 \times 0.43 \times \sin 45^\circ = 3.3 \times 3.3 \times 0.43 \times 0.707 = 3.33\ \mathrm{N}$$

Q: A solenoid has 400 turns, length $$l = 0.5\ \mathrm{m}$$, and cross-sectional radius $$r = 2.0\ \mathrm{cm}. If a $$steady current $$I = 0.8\ \mathrm{A}$$ flows, what is the magnitude of the magnetic field inside the solenoid?

$$B = \mu_0$ n I = 4\pi \times 10$$^{-7}$$ \times \frac{400}{0.5} \times 0.8 = 8.05 \times 10$$^{-4}$$\ \mathrm{T}$$

Q: A circuit has a resistor $$R = 4.5\ \Omega$$ and a battery of $$V = 9\ \mathrm{V}$$, with a current $$I = 2.0\ \mathrm{A}$$ flowing. What is the power emitted by the resistor?

$$P = I^2$ R = (2.0)^2$ \times 4.5 = 18\ \mathrm{W}$$

Q: A circuit contains two resistors in parallel: $$R_1 = 7.1$$\ \Omega$$ and R_2$ = 6.8\ \Omega$$, connected to a $$10.1\ \mathrm{V}$$ battery. What is the equivalent resistance?

$$R_{eq} = \frac{R_1$ R_2$}{R_1$ + R_2$} = \frac{7.1 \times 6.8}{7.1 + 6.8} = 3.47\ \Omega$$

Q: A circuit has a length $$l = 4.0\ \mathrm{cm}$$ and width $$w = 2.0\ \mathrm{cm}. $$The magnetic field increases from $$0.01\ \mathrm{T} to$$ $$0.03\ \mathrm{T} in$$ $$1.5\ \mathrm{s}. $$What is the magnitude of the induced EMF?

$$\mathcal{E} = \frac{\Delta B}{\Delta t} \times A = \frac{0.03 - 0.01}{1.5} \times (0.04 \times 0.02) = 0.000213\ \mathrm{V}$$

Question 1

A rectangular current loop with long side $$l = 18\ \mathrm{cm}$$ and short side $$w = 7.2\ \mathrm{cm}$$ carries a current $$I = 0.5\ \mathrm{A}. $$What is the magnitude of the magnetic dipole moment of the loop?

Accepted Answer

$$m = I 	imes l 	imes w = 0.5 	imes 0.18 	imes 0.072 = 0.00648\ \mathrm{A\cdot m^2$}$$

Question 2

An electron moves with velocity $$\vec{v} = 1.5 	imes 10^6$\ \mathrm{m/s}$$ through a region with a uniform magnetic field $$\vec{B} = 1.3\ \mathrm{T}. $$What is the magnitude of the Lorentz force acting on the electron?

Accepted Answer

$$F = |q|vB = 1.6 	imes 10$$^{-19}$$ 	imes 1.5 	imes 10^6$ 	imes 1.3 = 3.12 	imes 10$$^{-13}$$\ \mathrm{N}$$

Question 3

A straight wire of length $$L = 3.3\ \mathrm{m}$$ carries a current $$I = 3.3\ \mathrm{A}$$ and is placed in a uniform magnetic field $$B = 0.43\ \mathrm{T} at an $$angle $$	heta = 45^\circ to $$the field. What is the magnitude of the force on the wire?

Accepted Answer

$$F = I L B \sin	heta = 3.3 	imes 3.3 	imes 0.43 	imes \sin 45^\circ = 3.3 	imes 3.3 	imes 0.43 	imes 0.707 = 3.33\ \mathrm{N}$$

Question 4

Two parallel wires are separated by $$d = 10.0\ \mathrm{cm}$$ and each carries a current $$I = 0.5\ \mathrm{A}$$ out of the page. What is the direction of the magnetic force between the wires?

Accepted Answer

The wires attract each other.

Question 5

A solenoid has 400 turns, length $$l = 0.5\ \mathrm{m}$$, and cross-sectional radius $$r = 2.0\ \mathrm{cm}. If a $$steady current $$I = 0.8\ \mathrm{A}$$ flows, what is the magnitude of the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I = 4\pi 	imes 10$$^{-7}$$ 	imes \frac{400}{0.5} 	imes 0.8 = 8.05 	imes 10$$^{-4}$$\ \mathrm{T}$$

Question 6

A rectangular loop with sides $$a = 0.38\ \mathrm{m}$$ and $$b = 0.15\ \mathrm{m}$$ carries a current $$I = 4.5\ \mathrm{A}$$ counterclockwise. What is the direction of the area vector of the loop?

Accepted Answer

Out of the page

Question 7

A circuit has a resistor $$R = 4.5\ \Omega$$ and a battery of $$V = 9\ \mathrm{V}$$, with a current $$I = 2.0\ \mathrm{A}$$ flowing. What is the power emitted by the resistor?

Accepted Answer

$$P = I^2$ R = (2.0)^2$ 	imes 4.5 = 18\ \mathrm{W}$$

Question 8

A circuit contains two resistors in series: $$R_1 = 7.1$$\ \Omega$$ and R_2$ = 6.8\ \Omega$$, connected to a $$10.1\ \mathrm{V}$$ battery. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ = 7.1 + 6.8 = 13.9\ \Omega$$

Question 9

A circuit contains two resistors in parallel: $$R_1 = 7.1$$\ \Omega$$ and R_2$ = 6.8\ \Omega$$, connected to a $$10.1\ \mathrm{V}$$ battery. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = \frac{R_1$ R_2$}{R_1$ + R_2$} = \frac{7.1 	imes 6.8}{7.1 + 6.8} = 3.47\ \Omega$$

Question 10

A circuit has a length $$l = 4.0\ \mathrm{cm}$$ and width $$w = 2.0\ \mathrm{cm}. $$The magnetic field increases from $$0.01\ \mathrm{T} to$$ $$0.03\ \mathrm{T} in$$ $$1.5\ \mathrm{s}. $$What is the magnitude of the induced EMF?

Accepted Answer

$$\mathcal{E} = \frac{\Delta B}{\Delta t} 	imes A = \frac{0.03 - 0.01}{1.5} 	imes (0.04 	imes 0.02) = 0.000213\ \mathrm{V}$$

Question 11

A battery provides $$9\ \mathrm{V} to a $$resistor $$R = 4.5\ \Omega$$ with a current $$I = 2.0\ \mathrm{A}. If $$the resistance is doubled, what is the new current?

Accepted Answer

$$I = \frac{V}{2R} = \frac{9}{9} = 1.0\ \mathrm{A}$$

Question 12

A loop of wire with area $$A is in a $$region where the magnetic field $$B$$ increases at a constant rate. What is the direction of the induced current in the loop?

Accepted Answer

The induced current flows to oppose the increase in magnetic flux (Lenz's Law).

Question 13

A circuit contains three identical resistors $$R = 4.5\ \Omega in $$parallel, connected to a $$10.0\ \mathrm{V}$$ battery. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = \frac{R}{3} = \frac{4.5}{3} = 1.5\ \Omega$$

Question 14

A $$4.0\ \mathrm{A}$$ current moves from the negative to the positive terminal of a $$10.0\ \mathrm{V}$$ EMF through a resistor $$R = 1.0\ \Omega. $$What is the potential drop across the resistor?

Accepted Answer

$$V = I R = 4.0 	imes 1.0 = 4.0\ \mathrm{V}$$

Question 15

A light bulb in a circuit is rated at $$40\ \mathrm{W}$$ when the switch is closed and the EMF is $$11.0\ \mathrm{V}. $$What is the current through the bulb?

Accepted Answer

$$I = \frac{P}{V} = \frac{40}{11.0} = 3.64\ \mathrm{A}$$

Question 16

A solenoid has $$N = 400$$ turns, length $$l = 0.5\ \mathrm{m}$$, and radius $$r = 2.0\ \mathrm{cm}. $$What is its inductance?

Accepted Answer

$$L = \mu_0$ N^2$ A / l = 4\pi 	imes 10$$^{-7}$$ 	imes 400^2$ 	imes \pi 	imes (0.02)^2$ / 0.5 = 8.06 	imes 10$$^{-4}$$\ \mathrm{H}$$

Question 17

A rectangular loop with area $$A is $$rotated in a uniform magnetic field $$B at an $$angle $$	heta. $$What is the torque on the loop?

Accepted Answer

$$	au = m B \sin	heta$$

Magnetic Fields, Forces, and Circuits: Study Notes for PHYS112 Practice Exam

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