Question 1

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

Accepted Answer

$$E = \dfrac{q r}{4\pi\$$epsilon_0$$ R^3$}$$

Question 2

Which of the following correctly expresses the energy stored in a parallel-plate capacitor with charge $$Q$$ and capacitance $$C$$?

Accepted Answer

$$U = \dfrac{Q^2$}{2C}$$

Question 3

A wire of length $$L$$ and cross-sectional area $$A$$ has a resistivity $$\rho. $$What is the resistance $$R of $$the wire?

Accepted Answer

$$R = \dfrac{\rho L}{A}$$

Question 4

A charged particle moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the magnitude of the magnetic force acting on the particle?

Accepted Answer

$$F = qvB$$

Question 5

Which equation gives the electric field just outside a charged conductor with surface charge density $$\sigma$$?

Accepted Answer

$$E = \dfrac{\sigma}{\$$epsilon_0$$}$$

Question 6

A parallel-plate capacitor is filled with a dielectric material of constant $$K. $$How does the capacitance change compared to the original capacitance $$C_0$$?

Accepted Answer

$$C = K C_0$

Question 7

A resistor of resistance $$R is $$connected to a battery of emf $$E$$ and internal resistance $$r. $$What is the terminal voltage $$V_{ab}$$ across the resistor?

Accepted Answer

$$V_{ab} = E - Ir$$

Question 8

Which of the following is the correct expression for the energy density $$u in an $$electric field $$E$$?

Accepted Answer

$$u = \dfrac{1}{2} \$$epsilon_0$$ E^2$

Question 9

A charged particle moves in a circle of radius $$r in a $$uniform magnetic field $$B. $$What is the period $$T of $$its motion?

Accepted Answer

$$T = \dfrac{2\pi m}{qB}$$

Question 10

Which of the following correctly expresses the magnetic field at the center of a circular loop of radius $$R$$ carrying current $$I$$?

Accepted Answer

$$B = \dfrac{\mu_0$ I}{2R}$$

Question 11

A solenoid has $$n$$ turns per unit length and carries a current $$I. $$What is the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I$$

Question 12

A capacitor of capacitance $$C is $$charged to a voltage $$V. $$What is the total energy stored in the capacitor?

Accepted Answer

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

Question 13

A long straight wire carries a current $$I. $$What is the magnitude of the magnetic field at a distance $$r$$ from the wire?

Accepted Answer

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

Question 14

Which of the following is the correct form of Faraday's law of induction for a coil with $$N$$ turns?

Accepted Answer

$$E = -N \dfrac{d\Phi_B}{dt}$$

Question 15

A parallel-plate capacitor has plate area $$A$$ and separation $$d. $$What is its capacitance in vacuum?

Accepted Answer

$$C = \dfrac{\$$epsilon_0$$ A}{d}$$

Question 16

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

Accepted Answer

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

Question 17

Which of the following is the correct expression for the electric potential $$V at a $$distance $$r$$ from a point charge $$q$$?

Accepted Answer

$$V = \dfrac{q}{4\pi\$$epsilon_0$$ r}$$

Question 18

A resistor of resistance $$R$$ dissipates power $$P$$ when a current $$I$$ flows through it. Which equation gives the power?

Accepted Answer

$$P = I^2$ R$$

Question 19

A conducting loop of area $$A is $$placed in a uniform magnetic field $$B$$ that changes with time. What is the induced emf in the loop?

Accepted Answer

$$E = -\dfrac{d\Phi_B}{dt}$$

PHY2049 Formula Sheet and Study Guide: Chapters 21–36 (Electricity & Magnetism)

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