Q: A charged particle moves through a region where both electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ are present. The net force on the particle is given by which of the following expressions?

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

Question 1

A parallel-plate capacitor is filled with a dielectric material of relative permittivity $$\varepsilon_r. If $$the original capacitance without the dielectric is $$C_0$$, what is the new capacitance $$C$$ after inserting the dielectric?

Accepted Answer

$$C = C_0$ \varepsilon_r$$

Question 2

A long straight wire carries a current $$I. $$According to the Biot–Savart law, what is the magnitude of the magnetic field $$B at a $$distance $$r$$ from the wire?

Accepted Answer

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

Question 3

A point charge $$q is $$placed at the center of a spherical conducting shell of inner radius $$a$$ and outer radius $$b. $$What is the electric field inside the shell, for $$a \u003c r \u003c b$$?

Accepted Answer

$$E = 0$$

Question 4

A resistor of resistance $$R$$ and a capacitor of capacitance $$C$$ are connected in series to a battery of emf $$V_0. $$What is the charge $$Q(t) on $$the capacitor at time $$t$$ after the circuit is closed?

Accepted Answer

$$Q(t) = V_0$ C (1 - e$$^{-t/RC}$$)$$

Question 5

Which of the following best describes the physical meaning of electric potential at a point?

Accepted Answer

The work done by the electric field in moving a unit positive charge from infinity to that point

Question 6

A current $$I$$ flows through a rectangular loop of area $$A$$ placed in a uniform magnetic field $$B. $$What is the maximum torque $$	au_{max}$$ experienced by the loop?

Accepted Answer

$$	au_{max} = IAB$$

Question 7

A 12 V battery with internal resistance $$r = 1\ \Omega is $$connected to an external resistor $$R = 5\ \Omega. $$What is the terminal voltage $$V_{terminal} of $$the battery when current is flowing?

Accepted Answer

$$V_{terminal} = 12\ \mathrm{V} - I r$$

Question 8

Which of the following statements about Gauss’s law is correct?

Accepted Answer

It is most useful for systems with high symmetry (spherical, cylindrical, planar)

Question 9

A coil of wire with $$N$$ turns and area $$A is $$placed in a time-varying magnetic field $$B(t) = B_0$ \cos(\omega t). $$What is the maximum induced emf in the coil?

Accepted Answer

$$\mathcal{E}_{max} = N A B_0$ \omega$$

Question 10

A DC motor operates with a back emf $$E_b$$ and draws a current $$I$$ from a supply voltage $$V. If $$the resistance of the armature is $$R$$, what is the expression for the mechanical power output $$P_{mech}$$?

Accepted Answer

$$P_{mech} = I E_b$$

Question 11

A charged particle of 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

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

Question 12

Which of the following is a correct application of Lenz’s law?

Accepted Answer

The induced current always opposes the change in magnetic flux that produced it

Question 13

A circuit consists of a resistor $$R$$, inductor $$L$$, and capacitor $$C in $$series with an AC source of angular frequency $$\omega. At $$resonance, what is the impedance $$Z of $$the circuit?

Accepted Answer

$$Z = R$$

Question 14

A transformer has 100 turns on the primary coil and 500 turns on the secondary coil. If the input voltage is 120 V, what is the output voltage (ideal transformer)?

Accepted Answer

$$V_{out} = 600\ \mathrm{V}$$

Question 15

Which of the following best describes the function of a Hall effect sensor?

Accepted Answer

It detects the presence and magnitude of a magnetic field via the voltage developed across a conductor

Question 16

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

Accepted Answer

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

Question 17

Which of the following statements about Thevenin’s theorem is correct?

Accepted Answer

Any linear two-terminal circuit can be replaced by an equivalent voltage source in series with a resistor

Question 18

A capacitor stores energy in its electric field. What is the energy $$U$$ stored in a capacitor of capacitance $$C$$ charged to a voltage $$V$$?

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

A charged particle moves through a region where both electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ are present. The net force on the particle is given by which of the following expressions?

Accepted Answer

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

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