Q: A proton is released from rest at the surface of a sphere of radius $$R = 0.005 m $$and potential $$V = 1000 V. $$What is the charge $$Q on $$the sphere?

$$Q = 5.56 \times 10$$^{-11}$$ C

Q: A sodium ion ($$Na^+) is $$pumped from inside a cell (potential $$-70 mV) to $$outside (potential $$0 V). $$What is the work done to move one ion?

$$W = q \Delta V = (1.6 \times 10$$^{-19}$$ \text{ C})(70 \times 10$$^{-3}$$ \text{ V})$$

Question 1

Which of the following equations correctly gives the electric potential $$V at a $$distance $$r$$ from a point charge $$q in $$vacuum?

Accepted Answer

$$V = \frac{1}{4\pi\$$epsilon_0$$} \frac{q}{r}$$

Question 2

A proton is released from rest at the surface of a sphere of radius $$R = 0.005 m $$and potential $$V = 1000 V. $$What is the charge $$Q on $$the sphere?

Accepted Answer

$$Q = 5.56 	imes 10$$^{-11}$$ C

Question 3

Which of the following statements about equipotential surfaces is FALSE?

Accepted Answer

Equipotential surfaces can intersect each other.

Question 4

The electric field $$\vec{E} is $$related to the electric potential $$V by $$which of the following expressions?

Accepted Answer

$$\vec{E} = -
abla V$$

Question 5

A parallel plate capacitor has plates of area $$A$$ and separation $$d. $$What is the capacitance $$C$$?

Accepted Answer

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

Question 6

Which of the following best describes the potential difference $$\Delta V$$ between two points in a uniform electric field $$E$$ separated by distance $$d$$?

Accepted Answer

$$\Delta V = -Ed$$

Question 7

A battery is connected to a parallel plate capacitor, charging it to a potential difference $$V. If $$the area of the plates is doubled while keeping the separation the same, what happens to the capacitance?

Accepted Answer

It doubles.

Question 8

The energy stored in a capacitor with charge $$Q$$ and potential difference $$V is $$given by:

Accepted Answer

$$U = \frac{1}{2} QV$$

Question 9

Which of the following is a correct graphical representation of the electric potential $$V$$ between the plates of a parallel plate capacitor?

Accepted Answer

A straight line decreasing from the positive to the negative plate.

Question 10

For a system of point charges, the total electric potential at a point is:

Accepted Answer

The algebraic sum of the potentials due to each charge.

Question 11

A sodium ion ($$Na^+) is $$pumped from inside a cell (potential $$-70 mV) to $$outside (potential $$0 V). $$What is the work done to move one ion?

Accepted Answer

$$W = q \Delta V = (1.6 	imes 10$$^{-19}$$ 	ext{ C})(70 	imes 10$$^{-3}$$ 	ext{ V})$$

Question 12

Which of the following is TRUE about the relationship between electric field lines and equipotential surfaces?

Accepted Answer

Electric field lines are always perpendicular to equipotential surfaces.

Question 13

A proton is shot through a small hole in the negative plate of a parallel plate capacitor with a speed $$v_0. $$The capacitor is charged to a potential difference $$V. $$What determines whether the proton reaches the other side?

Accepted Answer

Whether its initial kinetic energy is greater than the potential energy difference $$qV.$$

Question 14

The potential at a distance $$z$$ above the center of a uniformly charged ring of radius $$R$$ and total charge $$Q is$$:

Accepted Answer

$$V = \frac{1}{4\pi\$$epsilon_0$$} \frac{Q}{\sqrt{R^2$ + z^2$}}$$

Question 15

If the electric field in a region is given by $$E_x = 1000x V/m$$, what is the potential $$V(x) if$$ $$V(0) = 0$$?

Accepted Answer

$$V(x) = -500x^2$ V

Question 16

Which configuration of four point charges (two positive, two negative) placed symmetrically about the x-axis gives $$V = 0 at $$all points on the x-axis?

Accepted Answer

The configuration where the charges above the x-axis are cancelled by those below.

Electric Potential, Equipotential Surfaces, and Capacitors: Study Notes

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