A certain charge Q is divided into two parts q and Q−q. How the charge Q and q must be related so that when q and (Q−q) is placed at a certain distance apart experience maximum electrostatic repulsion?
Q=2q
Q=3q
Q=4q
Q=4q+c
A
Q=3q
B
Q=4q+c
C
Q=2q
D
Q=4q
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Solution
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The electrostatic force of repulsion between the charge q and (Q−q) at separation r is given by F=14πε0q(Q−q)r2=14πε0qQ−q2r2 If F is maximum, then ∂F/∂q=0 i.e., 14πε0⋅(Q−2q)r2=0 As 14πε0r2 is constant, therefore Q−2q=0 or Q=2q
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