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: In the same circuit, the time constant $$\tau is $$given by $$\tau = \frac{L}{R}. If$$ $$L = 8.0 H $$and $$R = 16\ \Omega$$, what is the time constant?

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

Q: Two very long uniform lines of charge are parallel and separated by $$0.300 m. $$Each line has charge per unit length $$\lambda = +5.20\ \muC/m. $$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 $$L of $$the solenoid?

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

Q: A charged particle with charge $$q$$ moves with velocity $$\vec{v} in a $$magnetic field $$\vec{B}. $$What is the direction of the force $$\vec{F} on $$the particle?

$$\vec{F} = q \vec{v} \times \vec{B}$$, direction given by the right-hand rule for positive $$q$$ and left-hand rule for negative $$q$$

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, the time constant $$	au is $$given by $$	au = \frac{L}{R}. If$$ $$L = 8.0 H $$and $$R = 16\ \Omega$$, what is the time constant?

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Two very long insulated wires are perpendicular to each other in the same plane and carry equal currents. What is the direction of the net magnetic field at the intersection point?

Accepted Answer

The net magnetic field is perpendicular to the plane of the wires.

Question 7

A solenoid has 1200 turns, length $$\ell = 0.15 m$$, and cross-sectional area $$A = 25.0 mm$^2. $$What is the number of turns per unit length $$n$$?

Accepted Answer

$$n = \frac{N}{\ell} = \frac{1200}{0.15} = 8000 m$^{-1}$$

Question 8

What is the expression for the magnetic field inside a solenoid with $$n$$ turns per unit length and current $$I$$?

Accepted Answer

$$B = \mu_0$ n I$$

Question 9

Two very long uniform lines of charge are parallel and separated by $$0.300 m. $$Each line has charge per unit length $$\lambda = +5.20\ \muC/m. $$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 10

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

Accepted Answer

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

Question 11

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 $$L of $$the solenoid?

Accepted Answer

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

Question 12

A charged particle with charge $$q$$ moves with velocity $$\vec{v} in a $$magnetic field $$\vec{B}. $$What is the direction of the force $$\vec{F} on $$the particle?

Accepted Answer

$$\vec{F} = q \vec{v} 	imes \vec{B}$$, direction given by the right-hand rule for positive $$q$$ and left-hand rule for negative $$q$$

Question 13

In an $$RL$$ circuit, what is the expression for the current $$i(t) as a $$function of time after the circuit is closed?

Accepted Answer

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

Question 14

In an $$RL$$ circuit, what happens to the inductor at $$t = 0$$ and as $$t 	o \infty$$?

Accepted Answer

At $$t = 0$$, the inductor acts like a broken wire; as $$t 	o \infty$$, it acts like a wire.

Question 15

In an $$RC$$ circuit, what happens to the capacitor at $$t = 0$$ and as $$t 	o \infty$$?

Accepted Answer

At $$t = 0$$, the capacitor acts like a wire; as $$t 	o \infty$$, it acts like a broken wire.

Question 16

In the circuit shown, immediately after closing the switch, what is the current through the 20 mH inductor?

Accepted Answer

0 A

Question 17

In the same circuit, a long time after closing the switch, what is the current through the 5 $$\Omega$$ resistor?

Accepted Answer

0.32 A

Inductors and Self-Induced EMF: Step-by-Step Guidance

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