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?

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

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 $$L = 4.3\ \mathrm{m}$$ carries a current $$I = 3.3\ \mathrm{A}$$ and is placed in a uniform magnetic field $$B = 0.43\ \mathrm{T} at an $$angle $$\theta = 60^\circ to $$the field. What is the magnitude of the force on the wire?

$$F = I L B \sin\theta = 3.3 \times 4.3 \times 0.43 \times \sin 60^\circ = 5.33\ \mathrm{N}$$

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 $$I = 0.13\ \mathrm{A}$$ flows, what is the magnitude of the magnetic field inside the solenoid?

$$B = \mu_0$ n I = (4\pi \times 10$$^{-7}$$) \times \frac{400}{0.5} \times 0.13 = 8.74 \times 10$$^{-5}$$\ \mathrm{T}$$

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?

$$\mathcal{E} = \frac{\Delta B}{\Delta t} \times A = \frac{0.03 - 0.01}{1.5} \times (0.04 \times 0.02) = 5.33 \times 10$$^{-5}$$\ \mathrm{V}$$

Q: A battery provides $$9\ \mathrm{V} to a $$circuit with a $$4.5\ \Omega$$ resistor and a $$2.0\ \mathrm{A}$$ current. What is the power emitted by the resistor?

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

Q: A $$10.0\ \mathrm{V}$$ EMF is connected to three $$4.5\ \Omega$$ resistors in series. What is the current through the circuit?

$$I = V / R_{eq} = 10.0 / (4.5 \times 3) = 0.74\ \mathrm{A}$$

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

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

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 $$L = 4.3\ \mathrm{m}$$ carries a current $$I = 3.3\ \mathrm{A}$$ and is placed in a uniform magnetic field $$B = 0.43\ \mathrm{T} at an $$angle $$	heta = 60^\circ to $$the field. What is the magnitude of the force on the wire?

Accepted Answer

$$F = I L B \sin	heta = 3.3 	imes 4.3 	imes 0.43 	imes \sin 60^\circ = 5.33\ \mathrm{N}$$

Question 4

A solenoid has 400 turns, length $$l = 0.5\ \mathrm{m}$$, and cross-sectional radius $$r = 2.0\ \mathrm{cm}. If a $$steady current $$I = 0.13\ \mathrm{A}$$ flows, what is the magnitude of the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I = (4\pi 	imes 10$$^{-7}$$) 	imes \frac{400}{0.5} 	imes 0.13 = 8.74 	imes 10$$^{-5}$$\ \mathrm{T}$$

Question 5

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 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 (by the right-hand rule for current direction)

Question 7

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

$$\mathcal{E} = \frac{\Delta B}{\Delta t} 	imes A = \frac{0.03 - 0.01}{1.5} 	imes (0.04 	imes 0.02) = 5.33 	imes 10$$^{-5}$$\ \mathrm{V}$$

Question 8

A battery provides $$9\ \mathrm{V} to a $$circuit with a $$4.5\ \Omega$$ resistor and a $$2.0\ \mathrm{A}$$ current. What is the power emitted by the resistor?

Accepted Answer

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

Question 9

Three resistors $$R_1 = 7.1$$\ \Omega$$, R_2$ = 8.1\ \Omega$$, and $$R_3 = 6.1$$\ \Omega$$ are connected in series to a 10.1$$\ \mathrm{V}$$ EMF. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ + R_3$ = 7.1 + 8.1 + 6.1 = 21.3\ \Omega$$

Question 10

A $$10.0\ \mathrm{V}$$ EMF is connected to two resistors $$R_1 = 4.5$$\ \Omega$$ and R_2$ = 4.5\ \Omega in $$parallel. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = 1/(1/R_1$ + 1/R_2$) = 1/(1/4.5 + 1/4.5) = 2.25\ \Omega$$

Question 11

A $$10.0\ \mathrm{V}$$ EMF is connected to three $$4.5\ \Omega$$ resistors in series. What is the current through the circuit?

Accepted Answer

$$I = V / R_{eq} = 10.0 / (4.5 	imes 3) = 0.74\ \mathrm{A}$$

Question 12

A $$10.0\ \mathrm{V}$$ EMF is connected to two $$4.5\ \Omega$$ resistors in parallel. What is the current through each resistor?

Accepted Answer

$$I = V / R = 10.0 / 4.5 = 2.22\ \mathrm{A}$$

Question 13

A $$4.0\ \mathrm{A}$$ current moves from the negative to the positive terminal of a $$10.0\ \mathrm{V}$$ EMF through a resistor $$R_1 = 1.0$$\ \Omega$$. What is the potential drop across R_1$?

Accepted Answer

$$V = I R_1$ = 4.0 	imes 1.0 = 4.0\ \mathrm{V}$$

Question 14

A circuit has a $$10.1\ \mathrm{V}$$ EMF and three resistors $$R_1 = 7.1$$\ \Omega$$, R_2$ = 8.1\ \Omega$$, $$R_3 = 6.1$$\ \Omega$$ in series. What is the current through the circuit?

Accepted Answer

$$I = V / R_{eq} = 10.1 / 21.3 = 0.474\ \mathrm{A}$$

Question 15

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

Accepted Answer

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

Question 16

A circuit has a $$10.1\ \mathrm{V}$$ EMF and two resistors $$R_1 = 7.1$$\ \Omega$$, R_2$ = 8.1\ \Omega in $$parallel. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = 1/(1/7.1 + 1/8.1) = 3.77\ \Omega$$

Question 17

A $$10.1\ \mathrm{V}$$ EMF is connected to two resistors $$R_1 = 7.1$$\ \Omega$$ and R_2$ = 8.1\ \Omega in $$parallel. What is the current through $$R_1$$?

Accepted Answer

$$I_1 = V$$ / $$R_1 = 10.1 / 7.1 = 1.42$$\ \mathrm{A}$$

Question 18

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?

Accepted Answer

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

Magnetic Fields, Electromagnetic Induction, and Electric Circuits: Study Notes for PHYS112

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