Q: A charged particle moves in a region with both electric field $$\vec{E}$$ and magnetic field $$\vec{B}. $$Which equation gives the total force $$\vec{F} on $$the particle?

$$\vec{F} = q \vec{E} + q \vec{v} \times \vec{B}$$

Question 1

A parallel-plate capacitor is filled with a dielectric material of relative permittivity $$\varepsilon_r. If $$the plates have area $$A$$ and are separated by distance $$d$$, which equation correctly gives the capacitance $$C$$?

Accepted Answer

$$C = \frac{\$$varepsilon_0$$ \varepsilon_r A}{d}$$

Question 2

A point charge $$q is $$placed at the center of a spherical conducting shell of radius $$R. $$What is the electric field just outside the shell?

Accepted Answer

$$E = 0$$

Question 3

A resistor with resistance $$R is $$connected to a battery of EMF $$\mathcal{E}$$ and internal resistance $$r. $$What is the current $$I in $$the circuit?

Accepted Answer

$$I = \frac{\mathcal{E}}{R + r}$$

Question 4

Which of the following best describes the energy stored in a charged capacitor with capacitance $$C$$ and voltage $$V$$?

Accepted Answer

$$U = \frac{1}{2} CV^2$

Question 5

A long straight wire carries a current $$I. $$What is the magnetic field $$B at a $$distance $$r$$ from the wire according to Ampere’s law?

Accepted Answer

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

Question 6

A charged particle with charge $$q$$ and mass $$m$$ enters a region with a uniform magnetic field $$B$$ perpendicular to its velocity $$v. $$What is the radius $$r of $$its circular path?

Accepted Answer

$$r = \frac{mv}{qB}$$

Question 7

In a real-world scenario, a hospital uses a Hall effect sensor to measure blood flow. Which principle allows the sensor to detect the flow?

Accepted Answer

The sensor measures the voltage generated by the Lorentz force acting on moving charges in a magnetic field.

Question 8

A circuit contains a resistor $$R$$, a capacitor $$C$$, and a battery of voltage $$V_0. $$The capacitor is initially uncharged. What is the voltage across the capacitor after time $$t$$ during charging?

Accepted Answer

$$V_C = V_0$ \left(1 - e$$^{-t/RC}$$\right)$$

Question 9

A coil with $$N$$ turns and area $$A is $$placed in a time-varying magnetic field $$B(t). $$According to Faraday’s law, what is the induced EMF $$\mathcal{E}$$?

Accepted Answer

$$\mathcal{E} = -N A \frac{dB}{dt}$$

Question 10

A DC motor operates with a supply voltage $$V$$, resistance $$R$$, and back EMF $$E_b. $$What is the current $$I$$ through the motor?

Accepted Answer

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

Question 11

Which statement best describes the effect of inserting a dielectric into a charged, isolated capacitor?

Accepted Answer

The capacitance increases and the stored energy decreases.

Question 12

A patient receives an electric shock from a defibrillator. If the device delivers a voltage $$V$$ across the chest and the body resistance is $$R$$, what is the power dissipated in the body?

Accepted Answer

$$P = \frac{V^2$}{R}$$

Question 13

A circuit contains a resistor $$R$$, inductor $$L$$, and battery of voltage $$V_0. $$What is the current $$I(t) in $$the circuit at time $$t$$ after the switch is closed?

Accepted Answer

$$I(t) = \frac{V_0$}{R} \left(1 - e$$^{-tR/L}$$\right)$$

Question 14

A transformer has a primary coil with $$N_p$$ turns and a secondary coil with $$N_s$$ turns. If the input voltage is $$V_p$$, what is the output voltage $$V_s$$ for an ideal transformer?

Accepted Answer

$$V_s = V_p \frac{N_s}{N_p}$$

Question 15

A charged particle moves in a region with both electric field $$\vec{E}$$ and magnetic field $$\vec{B}. $$Which equation gives the total force $$\vec{F} on $$the particle?

Accepted Answer

$$\vec{F} = q \vec{E} + q \vec{v} 	imes \vec{B}$$

Question 16

A capacitor is used in a pacemaker circuit to deliver a pulse. If the capacitor is charged to voltage $$V$$ and has capacitance $$C$$, how much charge $$Q is $$delivered?

Accepted Answer

$$Q = C V$$

Question 17

Which of the following is a correct application of Gauss’s law for a uniformly charged sphere of radius $$R$$ and total charge $$Q$$?

Accepted Answer

Outside the sphere, $$E = \frac{Q}{4\pi \$$varepsilon_0$$ r^2$}$$ for $$r \u003e R$$

Question 18

A patient’s heart is monitored using an inductive sensor. Which property of the sensor changes as the heart beats?

Accepted Answer

The inductance of the sensor changes.

Question 19

A circuit contains a resistor $$R$$, capacitor $$C$$, and inductor $$L in $$series. If the circuit is driven by an AC voltage $$V(t) = V_0$ \cos(\omega t)$$, what is the impedance $$Z$$?

Accepted Answer

$$Z = \sqrt{R^2$ + (\omega L - \frac{1}{\omega C})^2$}$$

Comprehensive Study Guide: Electricity from Fundamentals to Advanced Engineering

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