Q: Given $$q = 1\ \mathrm{nC}$$, $$d = 1 \times 10$$^{-3}$$\ \mathrm{m}$$, and $$x = 1\ \mathrm{m}$$, what is the electric field at point $$P on $$the axis of the dipole?

$$E = 9 \times 10$$^{-3}$$\ \mathrm{N/C}$$

Q: Two long, straight wires are 8.0 mm apart and each carries a current of 5.0 A in the same direction. What is the magnitude and direction of the force per unit length between them?

$$F/L = 6.25 \times 10$$^{-4}$$\ \mathrm{N/m}$$, attractive

Question 1

A negatively charged rod is brought near an insulated metal sphere. Which of the following procedures will result in the sphere acquiring a net positive charge?

Accepted Answer

Bring the rod close to the sphere, ground the sphere briefly, then remove the ground and the rod.

Question 2

Using Gauss’ Law, what is the electric field outside a conducting sphere of radius $$R$$ carrying a total charge $$q at a $$distance $$r \u003e R$$ from its center?

Accepted Answer

$$E = \dfrac{q}{4\pi\$$epsilon_0$$ r^2$}$$

Question 3

For two conducting spheres with charges $$+q$$ and $$-q$$ separated by distance $$d$$, what is the approximate electric field at a point $$P$$ located a distance $$x$$ from the dipole center along the axis ($$x \gg d$$)?

Accepted Answer

$$E = \dfrac{1}{4\pi\$$epsilon_0$$} \dfrac{qd}{x^3$}$$

Question 4

Given $$q = 1\ \mathrm{nC}$$, $$d = 1 	imes 10$$^{-3}$$\ \mathrm{m}$$, and $$x = 1\ \mathrm{m}$$, what is the electric field at point $$P on $$the axis of the dipole?

Accepted Answer

$$E = 9 	imes 10$$^{-3}$$\ \mathrm{N/C}$$

Question 5

What is the electric potential at point $$P on $$the axis of the dipole described above?

Accepted Answer

$$V = 0$$

Question 6

For the circuit shown, what is the equivalent capacitance across the input terminals if $$C_1$$ and $$C_2$$ are in parallel and $$C_3 is in $$series with their combination?

Accepted Answer

$$C_{eq} = \left(\dfrac{1}{C_1$ + C_2$} + \dfrac{1}{C_3$}\$$right)^{-1}$$

Question 7

A positively charged particle moves in the $$+z$$ direction and experiences a magnetic force in the $$+y$$ direction. What is the direction of the $$x-$$component of the magnetic field at the particle’s position?

Accepted Answer

Negative $$x-$$direction

Question 8

Which of the following correctly states Gauss’s Law for electric and magnetic fields, and explains why the net magnetic flux through a closed surface is always zero?

Accepted Answer

$$\oint \vec{E} \cdot d\vec{A} = \dfrac{Q_{encl}}{\$$epsilon_0$$}$$ and $$\oint \vec{B} \cdot d\vec{A} = 0$$; because there are no magnetic monopoles.

Question 9

Two long, straight wires are 8.0 mm apart and each carries a current of 5.0 A in the same direction. What is the magnitude and direction of the force per unit length between them?

Accepted Answer

$$F/L = 6.25 	imes 10$$^{-4}$$\ \mathrm{N/m}$$, attractive

Question 10

A wire loop consists of two circular arcs of radii $$a = 7.5\ \mathrm{cm}$$ and $$b = 3.5\ \mathrm{cm}$$, subtending an angle $$	heta = 74.0^\circ at $$point $$P. If $$the current is $$I = 1.2\ \mathrm{A}$$, what is the direction of the net magnetic field at $$P$$?

Accepted Answer

Out of the page

Question 11

A light beam has wavelength $$400\ \mathrm{nm} in a $$material and $$525\ \mathrm{nm} in $$air. What is the index of refraction of the material?

Accepted Answer

$$n = 1.31$$

Question 12

A computer monitor draws $$1.8\ \mathrm{A}$$ from a $$230\ \mathrm{V}$$, $$50\ \mathrm{Hz}$$ supply. What is the amplitude of the current?

Accepted Answer

$$I_0 = 2.55$$\ \mathrm{A}$$

Question 13

The angular frequency of damped oscillations in an L-R-C circuit is $$\omega' = \sqrt{\dfrac{1}{LC} - \dfrac{R^2$}{4L^2$}}. $$What does $$R$$ represent in this equation?

Accepted Answer

Resistance of the circuit

Question 14

A convex lens has a focal length of $$20\ \mathrm{cm}$$ and is $$50\ \mathrm{cm}$$ from an object. What is the distance of the image from the lens?

Accepted Answer

$$s' = 33.3\ \mathrm{cm}$$

Question 15

Two sources emit light of wavelength $$500\ \mathrm{nm}$$ and are separated by $$1\ \mu\mathrm{m}. At $$what angle $$	heta$$ does the first intensity minimum occur?

Accepted Answer

$$	heta = 30^\circ$$

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