Question

Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

Options

• 3F/2

• 3F/4

• F

• 2F

Answer 1

3F/4

Explanation:

Consider two metallic spheres A and B both have charge q.

The force between two sphere will be

F =`"kq"^2/"r"^2` 

Charge will be applied to spheres A and C when sphere C comes into contact with sphere A = `"q"/2` 

Now When sphere C comes into contact with sphere B, a charge is applied to both spheres = `("q"+"q"/2)/2 = (3"q")/4`

Now, 

Then F₁ = `("kq"/2.(3"q")/4)/("r"^2/4)`

F2 = `(("k"3"q")/4(3"q")/4)/("r"^2/4)`

The force experienced by sphere C,

F' = F₂ - F₁ = `(("k"(3"q")/4-"k""q"/2))/("r"^2/4).(3"q")/4`

= `(3"kq"^2)/(4"r"^2)`

= `(3"F")/4`