Q: An inductor with inductance $$L = 0.260 H $$carries a current that is decreasing at a rate of $$\frac{di}{dt} = -0.0180 A/s. $$What is the self-induced emf across the inductor?

$$\mathcal{E}_{\text{ind}} = -L \frac{di}{dt} = -0.260 \times (-0.0180) = 4.68 mV$$

Q: What is the time constant $$\tau$$ for the above RL circuit?

$$\tau = \frac{L}{R} = \frac{8.0}{16} = 0.50 s$$

Q: Two very long insulated wires perpendicular to each other in the same plane carry currents. If the magnetic field at point P due to wire 1 is $$+25\ \muT$$ $$\hat{k}$$ and due to wire 2 is $$-16\ \muT$$ $$\hat{k}$$, what is the net magnetic field at P?

$$B_{\text{net}} = (25 - 16)\ \mu\text{T} = 9\ \mu\text{T}\ \hat{k}$$

Q: Two very long uniform lines of charge are parallel and separated by $$0.300 m. $$Each line has charge per unit length $$+5.20\ \muC/m. $$What is the magnitude of the force one line exerts on a $$0.0500 m $$section of the other?

$$F = \ell \lambda E = 0.0500 \times 5.20 \times 10$$^{-6}$$ \times 312 \times 10^3$ = 81 mN$$

Q: When the current in a long, straight, air-filled solenoid is changing at the rate of $$2000 A/s$$, the voltage across the solenoid is $$0.600 V. $$The solenoid has $$1200$$ turns and uniform cross-sectional area $$25.0 mm$^2. $$What is the inductance $$L$$?

$$L = \frac{\mathcal{E}_{\text{ind}}}{\frac{di}{dt}} = \frac{0.600}{2000} = 3.0 \times 10$$^{-4}$$ H

Q: What is the magnitude of the magnetic field $$B$$ inside the solenoid when the current is $$3.00 A$$?

$$B = \mu_0$ n I = 4\pi \times 10$$^{-7}$$ \times 7960 \times 3 = 30 mT$$

Question 1

An inductor with inductance $$L = 0.260 H $$carries a current that is decreasing at a rate of $$\frac{di}{dt} = -0.0180 A/s. $$What is the self-induced emf across the inductor?

Accepted Answer

$$\mathcal{E}_{	ext{ind}} = -L \frac{di}{dt} = -0.260 	imes (-0.0180) = 4.68 mV$$

Question 2

For the inductor described above, which end (a or b) is at a higher potential when the current is decreasing?

Accepted Answer

End a is at a higher potential than end b.

Question 3

A resistor and an inductor are connected in series to a battery with emf $$\mathcal{E} = 240 V. $$After a long time, the current in the circuit is 15.0 A. What is the resistance $$R of $$the circuit?

Accepted Answer

$$R = \frac{\mathcal{E}}{I} = \frac{240}{15.0} = 16\ \Omega$$

Question 4

In the same circuit, at time $$t = T$$, the current is 5.00 A and increasing at a rate of $$\frac{di}{dt} = 20.0 A/s. $$What is the inductance $$L$$?

Accepted Answer

$$L = \frac{\mathcal{E} - iR}{\frac{di}{dt}} = \frac{240 - 5.00 	imes 16}{20.0} = \frac{240 - 80}{20.0} = \frac{160}{20.0} = 8.0 H$$

Question 5

What is the time constant $$	au$$ for the above RL circuit?

Accepted Answer

$$	au = \frac{L}{R} = \frac{8.0}{16} = 0.50 s$$

Question 6

Two very long insulated wires perpendicular to each other in the same plane carry currents. If the magnetic field at point P due to wire 1 is $$+25\ \muT$$ $$\hat{k}$$ and due to wire 2 is $$-16\ \muT$$ $$\hat{k}$$, what is the net magnetic field at P?

Accepted Answer

$$B_{	ext{net}} = (25 - 16)\ \mu	ext{T} = 9\ \mu	ext{T}\ \hat{k}$$

Question 7

A long, straight wire carries a current $$I. $$What is the expression for the magnetic field at a distance $$r$$ from the wire?

Accepted Answer

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

Question 8

Two very long uniform lines of charge are parallel and separated by $$0.300 m. $$Each line has charge per unit length $$+5.20\ \muC/m. $$What is the magnitude of the force one line exerts on a $$0.0500 m $$section of the other?

Accepted Answer

$$F = \ell \lambda E = 0.0500 	imes 5.20 	imes 10$$^{-6}$$ 	imes 312 	imes 10^3$ = 81 mN$$

Question 9

When the current in a long, straight, air-filled solenoid is changing at the rate of $$2000 A/s$$, the voltage across the solenoid is $$0.600 V. $$The solenoid has $$1200$$ turns and uniform cross-sectional area $$25.0 mm$^2. $$What is the inductance $$L$$?

Accepted Answer

$$L = \frac{\mathcal{E}_{	ext{ind}}}{\frac{di}{dt}} = \frac{0.600}{2000} = 3.0 	imes 10$$^{-4}$$ H

Question 10

What is the magnitude of the magnetic field $$B$$ inside the solenoid when the current is $$3.00 A$$?

Accepted Answer

$$B = \mu_0$ n I = 4\pi 	imes 10$$^{-7}$$ 	imes 7960 	imes 3 = 30 mT$$

Question 11

A rectangular loop is placed near a long straight wire carrying current $$I. $$What is the direction of the net magnetic force on the loop?

Accepted Answer

To the right

Question 12

A semicircular wire of radius $$R$$ carries a current $$I. $$What is the direction of the magnetic field at the center of the semicircle?

Accepted Answer

Out of the plane of the figure

Question 13

In an RL circuit, what is the expression for the current as a function of time after the switch is closed?

Accepted Answer

$$i(t) = \frac{\mathcal{E}}{R} \left(1 - e$$^{-t/	au}$$ight)$$, where $$	au = \frac{L}{R}$$

Question 14

In an RC circuit, what is the limiting behavior of the capacitor immediately after the switch is closed?

Accepted Answer

The capacitor acts as a wire (no potential difference across it)

Question 15

In an RL circuit, what is the limiting behavior of the inductor immediately after the switch is closed?

Accepted Answer

The inductor acts as a broken wire (current is zero)

Question 16

In an RL circuit, what is the limiting behavior of the inductor after a long time?

Accepted Answer

The inductor acts as a wire (current is constant)

Question 17

In an RC circuit, what is the limiting behavior of the capacitor after a long time?

Accepted Answer

The capacitor acts as a broken wire (current is zero)

Question 18

A circuit contains two inductors and one resistor in series. The potential at three points is indicated: 0 V, -12 V, and 18 V. What is the potential at point P before the first inductor (18 mH)?

Accepted Answer

$$V_P = 0 + 12 + 18 = 30 V$$

Inductors, Magnetic Fields, and Circuits – Step-by-Step Physics Guidance

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