Q: For the sixth image, what is the total magnetic field at the center of the loop? $$B_{total} = \frac{\mu_0$ I}{2R} + \frac{\mu_0$ I}{2\pi r}$$

$$4.1 \times 10$$^{-4}$$\,T$$, into the page

Question 1

For the circuit shown in the first image, what is the equivalent capacitance between the terminals of the battery?

$$\frac{1}{C_{eq}} = \frac{1}{4.0\,\mu F} + \frac{1}{(2.0\,\mu F + 1.5\,\mu F)}$$

Accepted Answer

$$1.87\,\mu F$$

Question 2

How much total charge flows from the battery as the capacitors in the first circuit are being charged?

$$Q = C_{eq} V$$

Accepted Answer

$$22\,\mu C$$

Question 3

In the second image, immediately after the switch is closed, which bulbs are glowing and why?

Accepted Answer

Both bulbs glow because current flows through both as the capacitor charges.

Question 4

For the circuit in the second image, as time passes after the switch is closed, what happens to the brightness of the bulbs?

Accepted Answer

The brightness decreases as the current decreases.

Question 5

In the third image, immediately after the switch is moved to position b at $$t=0$$, what is the current through the resistor?

$$I = \frac{V}{R}$$

Accepted Answer

$$0.18\,A$$

Question 6

For the circuit in the third image, what is the charge on the capacitor at $$t = 50\,\mu s$$ after the switch is moved to position b?

$$Q = Q_0$ e$$^{-t/RC}$$

Accepted Answer

$$11\,\mu C$$

Question 7

In the fourth image, two solenoids of equal length and number of turns but different diameters carry equal and opposite currents. What is the magnetic field at the center of the inner solenoid?

Accepted Answer

It is zero because the fields from the two solenoids cancel.

Question 8

For the configuration in the fifth image, what is the direction of the net magnetic field at point 1?

Accepted Answer

Out of the page

Question 9

For the wires in the fifth image, what is the magnitude of the net magnetic field at point 2?

$$B = \frac{\mu_0$ I}{2\pi r_1$} + \frac{\mu_0$ I}{2\pi r_2$}$$

Accepted Answer

$$2.0 	imes 10$$^{-4}$$\,T$$

Question 10

A solenoid is 2.0 m long, has 1000 turns, and produces a 1.0 T field at its center. What current does it carry?

$$B = \mu_0$ \frac{N}{L} I$$

Accepted Answer

$$1.6\,kA$$

Question 11

For the sixth image, what is the total magnetic field at the center of the loop?

$$B_{total} = \frac{\mu_0$ I}{2R} + \frac{\mu_0$ I}{2\pi r}$$

Accepted Answer

$$4.1 	imes 10$$^{-4}$$\,T$$, into the page

Question 12

A compass is placed at a point where two perpendicular bar magnets create fields: one downward, one to the left. In which direction will the compass point?

Accepted Answer

Down and to the left

Question 13

A capacitor of $$2.0\,\mu F is $$charged to $$9.0\,V$$ and then discharged through a $$50\,\Omega$$ resistor. What is the time constant $$	au$$ for this circuit?

$$	au = RC$$

Accepted Answer

$$100\,\mu s$$

Question 14

In a discharging RC circuit, after a time equal to one time constant $$	au$$, what fraction of the initial charge remains on the capacitor?

$$Q = Q_0$ e$$^{-1}$$

Accepted Answer

$$1/e$$

Question 15

Which of the following statements about the magnetic field inside a long solenoid is correct?

Accepted Answer

It is zero if the current is zero.

Question 16

If the current in a solenoid is doubled, what happens to the magnetic field at its center?

$$B = \mu_0$ \frac{N}{L} I$$

Accepted Answer

It doubles.

Capacitors, Circuits, and Magnetic Fields: Step-by-Step Physics Guidance

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