Q: A lightning bolt transfers $$10^4 C of $$charge in $$0.01 s. $$What is the average current?

$$I = \frac{10^4$}{0.01} = 1 \times 10^6$ A

Q: A real-world scenario: In a hospital, a defibrillator uses a capacitor to deliver a pulse of energy to a patient's heart. If the capacitor has a capacitance of $$200 \muF $$and is charged to $$3000 V$$, how much energy is stored?

$$U = \frac{1}{2} C V^2$ = \frac{1}{2} \times 200 \times 10$$^{-6}$$ \times (3000)^2$ = 900 J$$

Question 1

Which of the following best describes Gauss's Law for electricity?

Accepted Answer

The net electric flux through a closed surface is proportional to the total charge enclosed by the surface.

Question 2

A point charge $$q is $$placed at the center of a spherical conducting shell of radius $$R. $$What is the electric field at a distance $$r$$ from the center, where $$r \u003c R$$?

Accepted Answer

$$E = \frac{1}{4\pi\$$varepsilon_0$$} \frac{q}{r^2$}$$

Question 3

Which equation represents the relationship between electric field $$\vec{E}$$ and electric potential $$V$$?

Accepted Answer

$$\vec{E} = -
abla V$$

Question 4

A parallel plate capacitor with plate area $$A$$ and separation $$d is $$filled with a dielectric of dielectric constant $$\kappa. $$What is the capacitance?

Accepted Answer

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

Question 5

A resistor of resistance $$R$$ and a capacitor of capacitance $$C$$ are connected in series to a battery of voltage $$V_0. $$What is the charge on the capacitor after a long time?

Accepted Answer

$$Q = C V_0$

Question 6

Which of the following statements about magnetic fields is correct?

Accepted Answer

Magnetic field lines always form closed loops and never begin or end at a charge.

Question 7

A wire carries a current $$I$$ and is placed in a uniform magnetic field $$\vec{B}. $$What is the force per unit length on the wire if it is perpendicular to the field?

Accepted Answer

$$F/L = I B$$

Question 8

A solenoid of length $$l$$, with $$N$$ turns, carries a current $$I. $$What is the magnetic field inside the solenoid?

Accepted Answer

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

Question 9

Which of the following is the correct form of Faraday's Law of electromagnetic induction?

Accepted Answer

$$\mathcal{E} = -\frac{d\Phi_B}{dt}$$

Question 10

A charged particle with charge $$q$$ and mass $$m$$ moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the radius of its circular path?

Accepted Answer

$$r = \frac{m v}{q B}$$

Question 11

Which of the following best describes the physical meaning of Maxwell's equations?

Accepted Answer

They describe how electric and magnetic fields are generated and altered by charges and currents.

Question 12

A circuit contains a resistor $$R$$, an inductor $$L$$, and a battery of voltage $$V_0$$ connected in series. What is the current in the circuit a long time after the switch is closed?

Accepted Answer

$$I = \frac{V_0$}{R}$$

Question 13

Which of the following is the correct expression for the energy stored in a capacitor with capacitance $$C$$ and voltage $$V$$?

Accepted Answer

$$U = \frac{1}{2} C V^2$

Question 14

A real-world application: In MRI machines, strong magnetic fields are used to align nuclear spins. Which law explains the creation of these magnetic fields by electric currents?

Accepted Answer

Ampère's Law

Question 15

A lightning bolt transfers $$10^4 C of $$charge in $$0.01 s. $$What is the average current?

Accepted Answer

$$I = \frac{10^4$}{0.01} = 1 	imes 10^6$ A

Question 16

A metal rod of length $$l$$ moves with velocity $$v$$ perpendicular to a uniform magnetic field $$B. $$What is the induced emf across the ends of the rod?

Accepted Answer

$$\mathcal{E} = B l v$$

Question 17

Which of the following is the correct expression for the force between two parallel current-carrying wires separated by distance $$d$$?

Accepted Answer

$$F = \frac{\mu_0$ I_1$ I_2$ l}{2\pi d}$$

Question 18

A real-world scenario: In a hospital, a defibrillator uses a capacitor to deliver a pulse of energy to a patient's heart. If the capacitor has a capacitance of $$200 \muF $$and is charged to $$3000 V$$, how much energy is stored?

Accepted Answer

$$U = \frac{1}{2} C V^2$ = \frac{1}{2} 	imes 200 	imes 10$$^{-6}$$ 	imes (3000)^2$ = 900 J$$

Question 19

Which of the following is the correct expression for the speed of electromagnetic waves in vacuum?

Accepted Answer

$$c = \frac{1}{\sqrt{\mu_0$ \$$varepsilon_0$$}}$$

PHYS 231: Electricity & Magnetism – Syllabus and Course Structure

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