Question

how does the electric potential energy between two positively charged particles change if the distance between them is tripled?
a. it is increased by a factor of 9.
b. it is reduced by a factor of 3.
c. it is increased by a factor of 3.
d. it is reduced by a factor of 9.

Explanation:

Step1: Recall the formula for electric potential energy

The electric potential energy \(U\) between two charges \(q_1\) and \(q_2\) separated by a distance \(r\) is given by \(U=\frac{kq_1q_2}{r}\), where \(k\) is a constant.

Step2: Analyze the effect of tripling the distance

Let the initial distance be \(r_1 = r\) and the final distance be \(r_2=3r\). The initial potential energy \(U_1=\frac{kq_1q_2}{r}\), and the final potential energy \(U_2=\frac{kq_1q_2}{3r}\).
We can find the ratio \(\frac{U_2}{U_1}=\frac{\frac{kq_1q_2}{3r}}{\frac{kq_1q_2}{r}}=\frac{1}{3}\)

Answer:

B. It is reduced by a factor of 3.