Question

Three point charges are placed at the vertices of an equilateral triangle of side l= 0.05 m . If these charges are displaced to the mid points a' , b' and c' respectively. Find the work done in shifting the charges to new location

Answer 1

The total work done will be 54 x 10⁸ J

Explanation :

Given ,

charge of each particles, q = 1 C

Length of each arm of triangle, l = 0.05

So, initial potential energy of the system,

U₁ = [(qxq) + (qxq) + (qxq)]/4πε₀l

=> U₁ = 3/4πε₀(0.05)

=> U₁ = 60/4πε₀ = 60 x 9 x 10⁹

=> U₁ = 54 x 10⁸ J

Again when the charges are moved to mid points they form another equilateral triangle with side l/2

Hence new potential energy,

U₂ = [(qxq) + (qxq) + (qxq)]/4πε₀(l/2)

=> U₂ = 2 x 3/4πε₀(0.05) = 2 x 54 x 10⁸  = 108 x 10⁸ J

So total work done,

W = U₂ - U₁

=> W = 108 x 10⁸ - 54 x 10⁸

=> W = 54 x 10⁸ J

Hence the total work done will be 54 x 10⁸ J