Question

The separation between the two charges $+q$ and $-q$ becomes double. The value of force will be:

• A. two fold
• B. half
• C. four fold
• D. one fourth

Answer 1

Answer: (D)

one fourth

Answer 2

The force between two charges $q$ and $-q$ is $F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q \times-q}{r^{2}}=-\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{2}}$ where $r=$ separation between the charges $\therefore F'=\frac{1}{4 \pi \varepsilon_{0}} \frac{q \times-q}{r'^{2}}$ $=-\frac{1}{4 \pi \varepsilon_{0}} \times \frac{q}{(2 r)^{2}}$ $\left(\because r'=2 r\right)$ $=\frac{1}{4} \,F$