Q: Which of the following is the correct form of Gauss's Law for electricity in differential form?

$$\nabla \cdot \vec{E} = \frac{\rho}{\$$epsilon_0$$}$$

Question 1

A parallel plate capacitor is part of a circuit with current flowing. Two surfaces connect to the same closed curve: surface 1 is flat, and surface 2 is curved. The wire with the current in it passes through surface 2, but not through surface 1. What is the value of the conduction current $$I_{through}$$ and the displacement current $$I_{disp}$$ through surface 1?

Accepted Answer

$$I_{through} = 0$$, $$I_{disp} = I_{through}$$

Question 2

Consider a circular parallel plate capacitor with radius $$R$$ that is charging. Three concentric circular surfaces are labeled A, B, and C, with radii $$R/2$$, $$R$$, and $$3R/2$$ respectively. Rank the electric flux through these surfaces from least to greatest.

Accepted Answer

$$\Phi_C \u003c \Phi_A = \Phi_B$$

Question 3

A circular parallel plate capacitor with radius $$R is $$charging. The magnetic field at a radius $$r = R/2$$ from the center is $$B_1. $$How does the magnetic field at $$r = R$$ ($$B_2) $$compare to $$B_1$$?

Accepted Answer

$$B_2$$ = \frac{1}{2}$$B_1$$

Question 4

Which of the following is the correct form of Ampère-Maxwell's Law in integral form?

Accepted Answer

$$\oint \vec{B} \cdot d\vec{l} = \mu_0$ I_{encl} + \mu_0$ \$$epsilon_0$$ \frac{d\Phi_E}{dt}$$

Question 5

A battery is connected in series to two wires with resistance. If the resistance of wire 1 is greater than the resistance of wire 2, how does the power dissipated in wire 1 ($$P_1) $$compare to wire 2 ($$P_2$$)?

Accepted Answer

$$P_1$$ \u003e $$P_2$$

Question 6

Three identical bulbs are connected to a battery in series. The battery emf is $$\mathcal{E}_{bat}$$, and the potential across a bulb is $$V_{bulb}. $$What is $$V_{bulb} in $$terms of $$\mathcal{E}_{bat}$$?

Accepted Answer

$$V_{bulb} = \frac{\mathcal{E}_{bat}}{3}$$

Question 7

Three identical bulbs are connected to a battery in parallel. The battery emf is $$\mathcal{E}_{bat}$$, and the potential across a bulb is $$V_{bulb}. $$What is $$V_{bulb} in $$terms of $$\mathcal{E}_{bat}$$?

Accepted Answer

$$V_{bulb} = \mathcal{E}_{bat}$$

Question 8

Consider two setups with three identical bulbs: one in series and one in parallel, each with identical batteries. If the power dissipated by a bulb in series is $$P_s$$ and in parallel is $$P_p$$, what is the ratio $$\frac{P_p}{P_s}$$?

Accepted Answer

$$\frac{P_p}{P_s} = 9$$

Question 9

A real battery has an internal resistance $$r. $$Which equation gives the terminal voltage $$\Delta V_{bat} in $$terms of emf $$\mathcal{E}$$ and current $$I$$?

Accepted Answer

$$\Delta V_{bat} = \mathcal{E} - Ir$$

Question 10

If you short circuit a battery with emf $$6.2\,\mathrm{V}$$ and internal resistance $$0.7\,\Omega$$, what is the power dissipated by the internal resistance?

Accepted Answer

$$P = 55\,\mathrm{W}$$

Question 11

Which of the following is the correct expression for the equivalent resistance of two resistors $$R_1$$ and $$R_2 in $$parallel?

Accepted Answer

$$R_{eq} = \frac{R_1$ R_2$}{R_1$ + R_2$}$$

Question 12

Which of the following is the correct form of Gauss's Law for electricity in differential form?

Accepted Answer

$$
abla \cdot \vec{E} = \frac{ho}{\$$epsilon_0$$}$$

Question 13

Which physical phenomenon is responsible for the production of X-rays in the electromagnetic spectrum?

Accepted Answer

Acceleration of electrons crashing into metal

Question 14

In a circuit, three identical bulbs are connected in parallel to a battery. If the current through the battery is $$I_{bat}$$, what is the current through each bulb $$I_{bulb}$$?

Accepted Answer

$$I_{bulb} = \frac{I_{bat}}{3}$$

Question 15

A current of $$2.0\,\mathrm{A}$$ flows in a circuit with two resistors ($$3\,\Omega$$ and $$1\,\Omega) $$and two batteries ($$20\,\mathrm{V}$$ and $$6\,\mathrm{V}). $$What is the emf $$\mathcal{E} of $$the battery at the bottom of the circuit if the positive terminal is on the right?

Accepted Answer

$$\mathcal{E} = 6\,\mathrm{V}$$

Question 16

Which of the following statements about the displacement current $$I_{disp} in a $$charging capacitor is correct?

Accepted Answer

It is equal to the conduction current outside the plates.

Question 17

Which of the following is the correct expression for the power dissipated by a resistor with potential difference $$\Delta V$$ and resistance $$R$$?

Accepted Answer

$$P = \frac{(\Delta V)^2$}{R}$$

Question 18

Which of the following is NOT a valid circuit element as described in the study materials?

Accepted Answer

Transformer

Electromagnetic Fields, Maxwell's Equations, and Fundamentals of Electric Circuits ch 28

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