Question 1

An electric dipole consists of charges $$+q$$ and $$-q$$ separated by a distance $$2a$$ and centered at the origin. Using the equation for the potential due to a point charge, derive the approximate expression for the electric potential $$V_R at a $$point $$R$$ located a distance $$x$$ from the dipole center along the x-axis, in the limit $$x \gg a.$$

Accepted Answer

$$V_R \approx -\frac{2qa}{4\pi\$$epsilon_0$$ x^2$}$$

Question 2

An electron is released from rest at $$x = 1.0\ \mathrm{m}$$ from a fixed dipole with $$q = 1\ \mathrm{nC}$$ and $$a = 0.1\ \mathrm{mm}. $$What is the electron’s speed when it is at $$x = 2.0\ \mathrm{m}$$ from the dipole? (Neglect all forces except the dipole’s field.)

Accepted Answer

$$v = \sqrt{\frac{4qa}{2\pi\$$epsilon_0$$ m_e} \left(\frac{1}{x_1$^2} - \frac{1}{x_2$^2}\right)}$$

Question 3

In the circuit shown, what is the current through the $$3\ \Omega$$ resistor?

Accepted Answer

$$I = 1.0\ \mathrm{A}$$

Question 4

A long straight wire carries a current $$i_1$$ and a rectangular loop a distance $$a$$ away, with sides of length $$b$$ and $$c$$, carries a current $$i_2. $$What is the net force on the loop due to $$i_1$$?

Accepted Answer

$$F = \frac{\mu_0$ i_1$ i_2$ b}{2\pi} \left( \frac{1}{a} - \frac{1}{a+c} \right)$$

Question 5

A solenoid has $$N = 1000$$ turns uniformly distributed over a length $$\ell = 40.0\ \mathrm{cm}. $$What current is needed to produce a magnetic field of $$1.00 	imes 10$$^{-4}$$\ \mathrm{T} at $$its center?

Accepted Answer

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

Question 6

For a solenoid, $$L = \frac{N \Phi_B}{I}. $$What does $$L$$ signify?

Accepted Answer

The inductance of the solenoid

Question 7

Unpolarized light passes through three polarizers with axes at $$0^\circ$$, $$60^\circ$$, and $$90^\circ. $$What fraction of the initial intensity $$I_0$$ emerges from the system?

Accepted Answer

$$\frac{1}{8}$$

Question 8

If the middle polarizer (at $$60^\circ) is $$removed, what fraction of $$I_0$$ emerges from the system?

Accepted Answer

$$0$$

Question 9

A transformer operates at $$V_p = 8.5\ \mathrm{kV} on $$the primary side and $$V_s = 120\ \mathrm{V} on $$the secondary side. What is the turns ratio $$N_p/N_s$$?

Accepted Answer

$$N_p/N_s = 70.8$$

Question 10

The average rate of energy consumption in the houses served by the transformer is $$18\ \mathrm{kW}. $$What is the rms current in the secondary coil?

Accepted Answer

$$I_s = \frac{P}{V_s}$$

Question 11

A convex mirror forms an image of an object. Is the image real or virtual?

Accepted Answer

Virtual

Question 12

Monochromatic light of wavelength $$\lambda = 620\ \mathrm{nm}$$ passes through a slit $$0.450\ \mathrm{mm}$$ wide. The diffraction pattern is observed on a screen $$3.00\ \mathrm{m}$$ away. At what distance from the center of the central maximum does the first minimum occur?

Accepted Answer

$$y = \frac{\lambda L}{a}$$

Question 13

Which of the following positions are within the central maximum for the single-slit diffraction described above?

Accepted Answer

Positions with $$|y| \u003c \frac{\lambda L}{a}$$

Question 14

A step-down transformer has a primary voltage of $$8.5\ \mathrm{kV}$$ and a secondary voltage of $$120\ \mathrm{V}. If $$the rms current in the secondary coil is $$150\ \mathrm{A}$$, what is the rms current in the primary coil?

Accepted Answer

$$I_p = \frac{V_s I_s}{V_p}$$

Question 15

A rectangular loop of wire with current $$i_2 is $$placed near a long straight wire carrying current $$i_1. If $$the loop is moved farther from the wire, what happens to the net force on the loop?

Accepted Answer

The net force decreases

Question 16

A convex mirror forms an image of an object. Is the image larger or smaller than the object?

Accepted Answer

Smaller

Question 17

Which equation correctly relates the energy stored in an inductor to the current flowing through it?

Accepted Answer

$$U = \frac{1}{2} L I^2$

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