Question

Two charges are a distance d apart. By what factor will the force between the charges change if the separation between them is quadrupled?

Select one:

a. 8

b. 4

c. 1/16

d. 1/4

Answer 1

C

Answer 2

Answer

1/ 16

as Force

, F1 = k q1 q2 / r^2

F2 = kq1 q2 / (4r)^2

F2 /F1 = 1/ 16

Answer 3

c. 1/16

as force F is proportional to 1/r^2

Answer 4

SOLUTION :

F is inversely proportional to  squared distance.

=> F = k / d^2 

So,

F1 = k  / (d1)^2 

F2 = k  / (d2)^2

=> F2/F1 = (d1)^2 / (d2)^2  = 1 / [ (d2 / d1)^2 ] = 1 / 4^2 = 1 / 16 

Hence, force between charges will be 1 / 16 times the initial force if distance is quadrupled : Option c  (ANSWER).