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Suppose the electric force on a proton due to some source charge q is F. Now suppose we increase the distance between the proton and q by a factor of 4. What is the force on the proton now in terms of the original force F?
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F=kq_1q_2/r^2

kq1q2 is fixed, thus F is inversely proportional to square of the distance.

Let initial F=kq_1q_2/r^2

now new distance = 4r

Thus, new F = F' = kq_1q_2/(4r)^2 = kq_1q_2/(16r2)

Thus, F'=F/16
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