Question

At one point in space, the electric potential energy of a 15 nC charge is 42 μJ . Part A) What is the electric potential at this point?
Express your answer to two significant figures and include the appropriate units.

Part B) If a 20 nC charge were placed at this point, what would its electric potential energy be?
Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

Part A:

$\rm 2.8\times 10^3\ Volts.$

Part B:

$\rm 5.6\times 10^{-5}\ J.$

Explanation:

Part A:

• Potential energy of charge at the given point, $\rm U=42\ \mu J=42\times 10^{-6}\ J.$

• Charge, $\rm q=15\ nC = 15\times 10^{-9}\ C.$

The potential energy at a point due to a charge is defined as

$\rm U=qV$.

where,

V = electric potential at that point.

Therefore,

$\rm V=\dfrac{U}{q}=\dfrac{42\times 10^{-6}}{15\times 10^{-9}}=2.8\times 10^3\ Volts.$

Part B:

Now, if the charge at that point is replaced with $\rm q_1 = 20\ nC = 20\times 10^{-9}\ C.$, then the electric potential energy at that point is given by

$\rm U=q_1V = 20\times 10^{-9}\times 2.8\times 10^3=5.6\times 10^{-5}\ J.$