Q: An isolated proton is released from rest at the positive plate of a parallel-plate capacitor with a potential difference of $$200\ \mathrm{V}. $$What is the proton’s speed when it reaches the negative plate?

$$1.9 \times 10^5$\ \mathrm{m/s}$$

Question 1

Which statement about dielectric polarization is incorrect?

Accepted Answer

Polarization creates free charges that move to cancel the external field.

Question 2

A copper wire of diameter $$2\ \mathrm{mm}$$ and length $$30\ \mathrm{cm}$$, cooled to $$3^\circ\mathrm{C}$$, is connected to a battery with a terminal voltage of $$9\ \mathrm{V}. $$How much power is dissipated by the wire? (Resistivity of copper at $$3^\circ\mathrm{C} is$$ $$1.68 	imes 10$$^{-8}$$\ \Omega\cdot\mathrm{m})$$

Accepted Answer

$$55\ \mathrm{W}$$

Question 3

A $$20\ \mathrm{V}$$ EMF source with a $$4\ \Omega$$ internal resistance is connected to a $$12\ \Omega$$ resistor. How much power is dissipated within the source?

Accepted Answer

$$6.3\ \mathrm{W}$$

Question 4

For a metallic conductor, increasing the temperature causes the resistivity to

Accepted Answer

increase.

Question 5

Refer to the diagram with two spheres of radius $$R$$ and charges $$Q_1$$ and $$Q_2$$ nearly touching. If the electric potential is zero at infinity, what must be the ratio $$Q_2$$/$$Q_1$$ for the total potential at point $$P to be $$zero?

Accepted Answer

$$\left[1 - \frac{R^2$}{r_1$^2}\right]^{-1/2}$$

Question 6

A parallel-plate capacitor with plate area $$A$$ and separation $$d is $$partially filled, along the separation distance, with a dielectric of constant $$K$$ and thickness $$3d/4. $$What is the capacitance?

Accepted Answer

$$\frac{4K}{K+3}\$$varepsilon_0$$\frac{A}{d}$$

Question 7

A proton initially moves along the line $$y = x (in $$the direction of increasing $$x$$ and $$y) $$and then enters a region with a uniform electric field pointing in the positive $$y-$$direction. What is the subsequent motion of the proton?

Accepted Answer

Motion with constant velocity in the $$x-$$direction and constant acceleration in the $$y-$$direction.

Question 8

Which statement about Gauss’ Law is incorrect?

Accepted Answer

Even with zero net enclosed charge, a nonuniform charge distribution inside a closed surface can produce a nonzero net electric flux over the entire surface.

Question 9

Refer to the circuit diagram with two capacitors $$C_1$$ and $$C_2 in $$parallel connected to an EMF source $$\mathcal{E}. $$Which statement is correct?

Accepted Answer

The capacitors have equal potential difference.

Question 10

A $$+4\ \mu\mathrm{C}$$ point charge is placed inside the cavity of a thick, hollow metallic conductor. The conductor is then given a net charge of $$+10\ \mu\mathrm{C}. $$What are the charges on the inner and outer surfaces of the conductor?

Accepted Answer

$$-4\ \mu\mathrm{C} on $$the inner surface and $$+14\ \mu\mathrm{C} on $$the outer surface.

Question 11

A non-conducting cube of side $$2\ \mathrm{m}$$ contains a spherical cavity of radius $$1\ \mathrm{m}. $$The cube has a uniform volume charge density of $$5\ \mu\mathrm{C}/\mathrm{m}^3. $$What is the total electric flux through the cube's outer surface?

Accepted Answer

$$40\ \mu\mathrm{V}\cdot\mathrm{m}$$

Question 12

In a region of space, the electric field is given by

$$\vec{E}(x, y, z) = (2Ax - B,\ -Ay + C,\ C)$$

where $$A$$, $$B$$, and $$C$$ are nonzero constants. The electric potential is such that $$V(0,0,0) = 0. $$Which of the following expressions for $$V(x,y,z) is $$correct?

Accepted Answer

$$V(x, y, z) = -Ax^2$ + Bx + \frac{1}{2}Ay^2$ - Cy - Cz$$

Question 13

An isolated proton is released from rest at the positive plate of a parallel-plate capacitor with a potential difference of $$200\ \mathrm{V}. $$What is the proton’s speed when it reaches the negative plate?

Accepted Answer

$$1.9 	imes 10^5$\ \mathrm{m/s}$$

Question 14

Two points located $$10\ \mathrm{cm}$$ and $$20\ \mathrm{cm}$$ from an infinite, uniformly charged wire have a potential difference of $$5.0\ \mathrm{V}. $$What is the magnitude of the wire’s linear charge density?

Accepted Answer

$$64\ \mathrm{pC/m}$$

Question 15

A spherical capacitor consists of two concentric spherical shells of radii $$r_a$$ and $$r_b$$ ($$r_b \u003e r_a$$), filled with a dielectric of permittivity $$\varepsilon. If $$the inner shell carries charge $$+Q$$ and the outer shell $$-Q$$, what is the radial component of the electric field for $$r \u003e r_b$$?

Accepted Answer

$$0$$

Question 16

An electric field of magnitude $$E is $$applied along a cylindrical metal wire of resistivity $$\rho$$, resulting in a current $$I. $$What is the diameter of the wire?

Accepted Answer

$$\left(\frac{4I}{\pi \rho E}\$$right)^{1/2}$$

Question 17

In the ground state of a hydrogen atom, the electron and proton are separated by an average distance of $$5.3 	imes 10$$^{-11}$$\ \mathrm{m}. $$What is the electrical potential energy, assuming zero potential at infinite separation?

Accepted Answer

$$-27.2\ \mathrm{eV}$$

Question 18

A uniform electric field of magnitude $$25\ \mathrm{V/m}$$ makes a $$30^\circ$$ angle with the normal to a $$10\ \mathrm{cm}$$ diameter circular disk. What is the electric flux through the disk?

Accepted Answer

$$0.68\ \mathrm{V\cdot m}$$

Question 19

A plastic rod is charged by friction so that it acquires an excess charge of $$-1.6\ \mu\mathrm{C}. $$Approximately how many electrons have been transferred to the rod?

Accepted Answer

$$10^{13}$$ electrons

Question 20

A $$25\ \mu\mathrm{F}$$ parallel-plate capacitor is connected to a $$200\ \mathrm{V}$$ battery. When the space between the plates is completely filled with Teflon (dielectric constant $$K = 2.2$$), what is the energy stored?

Accepted Answer

$$1.1\ \mathrm{J}$$

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