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 in the inductor?

$$\mathcal{E}_{\text{ind}} = -L \frac{di}{dt} = -0.260 \times (-0.0180) = 4.7 mV$$

Q: In the same circuit, what is the value of the inductance $$L$$?

$$L = \frac{240}{20.0} \times 0.667 = 8.0 H$$

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

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

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

$$F = \ell \lambda E = 5.0 \times 10$$^{-2}$$ \times 5.2 \times 10$$^{-6}$$ \times 312 \times 10$$^{3}$$ = 81 mN$$

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

$$L = \frac{\mathcal{E}_{\text{ind}}}{\frac{di}{dt}} = \frac{0.6}{2000} = 3 \times 10$$^{-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 in the inductor?

Accepted Answer

$$\mathcal{E}_{	ext{ind}} = -L \frac{di}{dt} = -0.260 	imes (-0.0180) = 4.7 mV$$

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 $$\mathcal{E} = 240 V. At$$ $$t = T$$, the current is $$5.00 A $$and increasing at $$20.0 A/s. $$After a long time, the current is $$15.0 A. $$What is the value of the resistance $$R$$?

Accepted Answer

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

Question 4

In the same circuit, what is the value of the inductance $$L$$?

Accepted Answer

$$L = \frac{240}{20.0} 	imes 0.667 = 8.0 H$$

Question 5

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

Accepted Answer

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

Question 6

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

$$F = \ell \lambda E = 5.0 	imes 10$$^{-2}$$ 	imes 5.2 	imes 10$$^{-6}$$ 	imes 312 	imes 10$$^{3}$$ = 81 mN$$

Question 7

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

Accepted Answer

$$L = \frac{\mathcal{E}_{	ext{ind}}}{\frac{di}{dt}} = \frac{0.6}{2000} = 3 	imes 10$$^{-4}$$ H

Question 8

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 9

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 along the vector sum of the individual fields, which is diagonal to the plane.

Question 10

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

Toward the wire (upward)

Question 11

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

Accepted Answer

Out of the plane of the figure

Question 12

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/(L/R)}$$\right)$$

Question 13

In an $$RL$$ circuit, what is the limiting behavior of the inductor as $$t 	o 0$$ and as $$t 	o \infty$$?

Accepted Answer

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

Question 14

In an $$RC$$ circuit, what is the limiting behavior of the capacitor as $$t 	o 0$$ and as $$t 	o \infty$$?

Accepted Answer

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

Question 15

A circuit contains a resistor, inductor, and capacitor. Immediately after closing the switch, what is the current through the inductor?

Accepted Answer

Zero, because the inductor initially blocks current.

Question 16

A circuit contains a resistor, inductor, and capacitor. A long time after closing the switch, what is the current through the capacitor?

Accepted Answer

Zero, because the capacitor acts like a broken wire when fully charged.

Question 17

In a circuit with two inductors and one resistor in series, the potential at three points is indicated as $$0 V$$, $$-12 V$$, and $$18 V. $$What is the potential at point $$P$$ before the first inductor?

Accepted Answer

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

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

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