How many times should the charge of one of the two point bodies be changed so that when the distance between

How many times should the charge of one of the two point bodies be changed so that when the distance between them increases by 16 times, the force of their interaction does not change?

To determine the amount of the required increase in the charge of one of the indicated point bodies, we use the equality: k * qk1 * q ^ 2 / rk2 = F = k * qn1 * q ^ 2 / rn ^ 2, whence we express: qk1 = qn1 * rk ^ 2 / rн ^ 2.

Variable relations: rc (final distance) = 16rn (initial distance).

Let’s make the calculation: qk1 = qn1 * rk ^ 2 / rn ^ 2 = qn1 * (16rn) ^ 2 / rn ^ 2 = qn1 * 256rn ^ 2 / rn ^ 2 = 256qn1.

Answer: The charge of one of the indicated point bodies needs to be increased 256 times.