Question

a positively charged test object is moving toward the positive source charge in an electric field.
a. its potential energy decreases
b. its potential energy increases
c. its potential energy stays the same
d. its potential energy becomes negative

Answer 1

Consider the equation for electric potential energy:\[U=\frac{1}{4 \pi \epsilon_{0}}\frac{q_{1}q_{2}}{r}\]
You can see that if q1 and q2 are positive, the energy is going to be positive. This eliminates answer (d).

More importantly, let's look at the relationship of U with r:\[U \varpropto\frac{1}{r}\]
Since U is dependent on r, this eliminates answer (c).

With this relationship, if r is decreased then U is going to increase. I would therefore choose answer (b).

Answer 2

Thank you! :) This helped a lot.