Question

Two charged particles are separated by 10 cm. suppose the charge on each particle is doubled. By what factor does the electric force between the particles change?

Answer 1

Answer:

The electric force increases by a factor of 4.

Explanation:

The electric force between two charges $q_1$ and $q_2$ separated a distance d can be calculated using Coulomb's Law:

$F=\frac{kq_1q_2}{d^2}$

where $k=9\times10^9Nm^2/C^2$ is the Coulomb constant.

If the value of each charge is doubled, then we will have a force between them which is:

$F'=\frac{k(2q_1)(2q_2)}{d^2}=4\frac{kq_1q_2}{d^2}=4F$

So the new force is 4 times larger than the original force.