Question

4.
Force between two identical spheres charged with
same charge is F. If 50% charge of one sphere is
transferred to the other sphere then the new force
will be :-
1)3/4F
2)3/8F
3)3/2F
4)NONE OF THESE ​

Answer 1

Given:

Initial force between two identical spheres charged with same charge = F

To Find:

New force between the two identical sphere when 50% charge from one sphere is transferred to the other sphere.

Answer:

Let the initial charge on the two identical charged spheres be:

$\rm q_1 = q_2 = q$

Initial force:

$\rm \implies F = \dfrac{kq_1q_2}{ {r}^{2} } \\ \\ \rm \implies F = \dfrac{k \times q \times q}{ {r}^{2} } \\ \\ \rm \implies F = \dfrac{kq ^{2} }{ {r}^{2} }$

When 50% of charge from one sphere is transferred to the other sphere charge on both the sphere:

$\rm {q}_{1}' = q - \dfrac{50}{100} q \\ \\ \rm {q}_{1}' = q - \dfrac{1}{2} q \\ \\ \rm {q}_{1}' = \dfrac{q}{2} \\ \\ \\ \rm {q}_{2}' = q + \dfrac{50}{100} q \\ \\ \rm {q}_{2}' = q + \dfrac{1}{2} q \\ \\ \rm {q}_{2}' = \dfrac{3}{2}q$

Let the final force be F':

$\rm \implies F' = \dfrac{kq_1'q_2'}{ {r}^{2} } \\ \\ \rm \implies F' = \dfrac{k \times \dfrac{q}{2} \times \dfrac{3q}{2} }{ {r}^{2} } \\ \\ \rm \implies F' = \dfrac{k \times \dfrac{3q ^{2} }{4} }{ {r}^{2} } \\ \\ \rm \implies F' = \dfrac{3}{4} \bigg( \dfrac{kq ^{2} }{ {r}^{2} } \bigg) \\ \\ \rm \implies F' = \dfrac{3}{4} F$

$\therefore$ New force between the two identical sphere when 50% charge from one sphere is transferred to the other sphere = $\sf \dfrac{3}{4} \ F$

Correct Option: $\boxed{\mathfrak{(1) \ \dfrac{3}{4} \ F}}$

Answer 2

F ∝ q1q2

F/F' = q×q/0.5q×1.5q

F/F' = 1/0.75

F' = 0.75F

F' = 3/4F