Exercises: Electric Potential

Which of the following best distinguishes electric potential $V$ from the electric field $E$?

A positive charge is moved opposite to the direction the electric force pushes it. What happens to its electric potential energy?

The work done by a constant force $F$ over a displacement $d$ is $W = Fd$. Which energy principle directly connects this to electric potential energy?

The electric potential at a distance $r$ from a point charge $q$ is given by $V = kq/r$, where $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$. What are the SI units of electric potential?

A point charge of $q = +5.0\ \mu\text{C}$ is fixed in space. Calculate the electric potential at a point $r = 0.30\ \text{m}$ from the charge. Use $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$.

A point charge of $q = -4.0\ \mu\text{C}$ is fixed in space. What is the electric potential at a distance of $r = 0.20\ \text{m}$ from the charge? Use $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$.

A charge of $q = +2.0\ \mu\text{C}$ is moved through a potential difference of $\Delta V = 500\ \text{V}$ (from low to high potential). How much work is done by an external agent in moving the charge?

A charge of $q = -3.0\ \mu\text{C}$ moves from a point at $V_A = 200\ \text{V}$ to a point at $V_B = 500\ \text{V}$. Calculate the work done by the electric force on this charge.

A $+10\ \mu\text{C}$ point charge is at the origin. At which distance from the charge is the electric potential equal to $9.0 \times 10^4\ \text{V}$? Use $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$.

A $-5.0\ \mu\text{C}$ charge is released from rest near a positive source charge where the electric potential is high. Which statement correctly describes what happens?

Looking at a diagram that shows electric field lines radiating outward from a positive point charge, where should the equipotential surfaces be drawn?

For the formula $V = kq/r$, as $r$ approaches infinity, $V$ approaches   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . This means the potential at infinity is taken as the   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   reference point, and the potential never equals zero at any   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   distance from a point charge.

A $+4.0\ \mu\text{C}$ charge starts at rest near another positive charge where the potential is $V_i = 6000\ \text{V}$. It is released and moves to a point where $V_f = 2000\ \text{V}$. Using conservation of energy, what is the kinetic energy gained by the charge?

An electron (charge $q = -1.6 \times 10^{-19}\ \text{C}$) is accelerated from rest through a potential difference of $\Delta V = 1000\ \text{V}$ in a cathode-ray tube.

What kinetic energy does the electron gain? Express your answer in joules.

A proton (charge $q = +1.6 \times 10^{-19}\ \text{C}$, mass $m = 1.67 \times 10^{-27}\ \text{kg}$) is released from rest at a point where the electric potential is $V_i = 800\ \text{V}$. It travels to a point where $V_f = 0\ \text{V}$.

Using conservation of energy, find the speed of the proton at the final point.

A student calculates the electric potential at a point near a $+6\ \mu\text{C}$ charge. Read their work and identify the error.

A student reasons about a negative charge near a positive source charge. Read their reasoning and identify the mistake.

Two point charges are fixed: $q_1 = +6.0\ \mu\text{C}$ at the origin, and $q_2 = -2.0\ \mu\text{C}$ at $x = 0.50\ \text{m}$. Calculate the electric potential at the point $x = 0.25\ \text{m}$ (midway between the two charges). Use $k = 9.0 \times 10^9\ \text{N·m}^2/\text{C}^2$.

A topographic map uses closely spaced contour lines to show steep terrain and widely spaced lines to show gentle slopes. Explain how this analogy applies to electric potential maps showing equipotential lines. In your explanation, describe what the "steepness" represents physically and how you could determine where the electric field is strongest from an equipotential map.