Question

Two conducting spherical shells A and B of radii R and 2R are kept far apart and charged to the same charge density σ. They are connected by a wire. Obtain an expression for final potential of shell A.

Answer 1

According to the question,

`Q_1/(4piR^2) = Q_2/(4 pi (2R)^2`

⇒ `Q_1/(R^2) = Q_2/(4R^2)`

⇒ `Q_1 = Q_2/4`

⇒ Q₂ = 4Q₁; If Q₁ = Q (say)

then Q₂ = 4Q

So, the total charge = 5Q

When the two spherical shells are connected by a wire after shifting of charge.

Now, V₁ = V₂

⇒ `(kalpha)/R = (k(5Q - alpha))/(2R)`

2α = 5Q − α

⇒ `alpha = (5Q)/3`

= `k/R xx 5/3 xx sigma xx 4 pi R^2`

= `1/(4 pi epsilon_0R) xx 5/3 xx sigma xx 4 pi R^2`

= `(5 sigma R)/(3 epsilon_0)`