two identical charged spheres

Electricity and Magnetism Level 3

If the charge on each of two identical tiny spheres is doubled while their distance is also doubled, their force of interaction will __________ . \text{\_\_\_\_\_\_\_\_\_\_}.

become halved double stay unchanged become quatered

Krishna Singh by Krishna Singh , 22, India

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1 solution

Tom Engelsman
May 28, 2020

By Coloumb's Law, we have F = k q 1 q 2 r 2 F = \frac{kq_{1}q_{2}}{r^2} with q 1 = q 2 = q q_{1}=q_{2}=q . If the charges and their separation are both doubled, then we obtain:

F = k ⋅ ( 2 q ) 2 ( 2 r ) 2 = k ( 4 q 2 ) 4 r 2 = k q 2 r 2 F = \frac{k \cdot (2q)^2}{(2r)^2} = \frac{k(4q^2)}{4r^2} = \boxed{\frac{kq^{2}}{r^2}}

Hence, no change in electrostatic force results under these conditions.

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