Question

(4) DUUT (1) dic (2)
If two charged particles of charge q and Q - 9
(Q is a constant) are kept at a distance of 1 m
from each other, the electrostatic force between
them is maximum for q = 9. The value of 1-0
is
(1) 1
(2)
-NI-
(3) 2
​

Answer 1

two charged particles of charge q and Q - q are kept at a distance of 1m from each other.

then, electrostatic force , F = Kq(Q-q)/1²

differentiating both sides with respect to q ,

dF/dq = K(Q - 2q)

equating dF/dq = 0,

so, K(Q - 2q) = 0 => q = Q/2

again, differentiating to check at q = Q/2, F will be maximum or not.

d²F/dq² = -2<0

so, force will be maximum at q = Q/2

hence, $q_0=\frac{Q}{2}$

now $1-\frac{q_0}{Q}$

= 1 - Q/2Q = 1/2

therefore, option (2) is correct.