Q: A proton is released from rest at the surface of a sphere with a radius of $$0.5\ \mathrm{cm}$$ and a potential of $$+1000\ \mathrm{V}. $$What is the charge $$Q on $$the sphere?

$$Q = 5.6 \times 10$$^{-9}$$\ \mathrm{C}$$

Question 1

A proton is released from rest at the surface of a sphere with a radius of $$0.5\ \mathrm{cm}$$ and a potential of $$+1000\ \mathrm{V}. $$What is the charge $$Q on $$the sphere?

Accepted Answer

$$Q = 5.6 	imes 10$$^{-9}$$\ \mathrm{C}$$

Question 2

Which of the following statements about electric potential $$V is $$correct?

Accepted Answer

The electric potential is a scalar quantity and exists everywhere in space.

Question 3

A positive charge $$q$$ moves from a region of potential $$V_1 to a $$region of higher potential $$V_2. $$What happens to its kinetic energy?

Accepted Answer

Its kinetic energy decreases.

Question 4

The electric potential at a distance $$r$$ from a point charge $$q is $$given by which of the following expressions?

Accepted Answer

$$V = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{q}{r}$$

Question 5

A thin, uniformly charged ring of radius $$R$$ carries total charge $$Q. $$What is the electric potential at a point on the axis of the ring, a distance $$z$$ from its center?

Accepted Answer

$$V = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{Q}{\sqrt{R^2$ + z^2$}}$$

Question 6

A negative charge $$-q is $$released from rest in a uniform electric field pointing to the right. What happens to its potential energy as it moves to the left?

Accepted Answer

Its potential energy increases (becomes less negative).

Question 7

Which of the following best describes the relationship between electric field lines and equipotential surfaces inside a parallel-plate capacitor?

Accepted Answer

Electric field lines are perpendicular to equipotential surfaces.

Question 8

Three electrons are placed in a line, equally spaced. The center electron is displaced slightly to the right. What will happen to it?

Accepted Answer

It will accelerate further to the right, away from the center, indicating unstable equilibrium.

Question 9

A proton is fired from far away toward a stationary glass sphere of radius $$0.5\ \mathrm{mm}$$ and charge $$+100\ \mathrm{nC}. $$What is the minimum initial kinetic energy required for the proton to just reach the surface of the sphere?

Accepted Answer

$$K_i = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{q_p Q}{r}$$

Question 10

A positive and a negative charge are released from rest in vacuum. As they move toward each other, what happens to the system's electric potential energy?

Accepted Answer

A negative potential energy becomes less negative.

Question 11

Which of the following is true about the electric potential energy $$U of $$two point charges $$q_1$$ and $$q_2$$ separated by distance $$r$$?

Accepted Answer

$$U = \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{q_1$ q_2$}{r}$$

Question 12

A proton moves through a potential difference of $$100\ \mathrm{V}$$, slowing down from an initial speed of $$2.0 	imes 10^5$\ \mathrm{m/s}. $$What is its final speed?

Accepted Answer

$$v_f = \sqrt{v_i^2$ - \dfrac{2e\Delta V}{m_p}}$$

Question 13

Which of the following is a correct statement about the zero point of electric potential?

Accepted Answer

The choice of where $$V = 0 is $$arbitrary and does not affect physical predictions.

Question 14

A water molecule (a permanent dipole) is aligned with an electric field. How much energy is needed to rotate it by $$90^\circ$$?

Accepted Answer

$$\Delta U = pE$$

Question 15

If a positive charge is released from rest, in which direction does it move?

Accepted Answer

Toward lower electric potential.

Question 16

The electric potential at a point due to multiple point charges is:

Accepted Answer

The algebraic sum of the potentials due to each charge.

Question 17

A parallel-plate capacitor has a voltage $$\Delta V$$ across plates separated by distance $$d. $$What is the electric field $$E$$ between the plates?

Accepted Answer

$$E = \dfrac{\Delta V}{d}$$

Question 18

Which of the following is true about the work done by the electric force when moving a charge between two points?

Accepted Answer

It depends only on the initial and final positions, not the path taken.

Question 19

A proton and an electron are released from rest $$100\ \mathrm{fm}$$ apart. What is the minimum speed each must have to escape each other?

Accepted Answer

$$v = \sqrt{\dfrac{1}{2m_e} \dfrac{1}{4\pi\$$varepsilon_0$$} \dfrac{e^2$}{r}}$$

Chapter 25: The Electric Potential – Study Notes

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