Three point charges 1C,2C,3C are placed at the corners of an eqiulateral triangle of side 1m. calculate the work done to move these charges to the corners of a smaller equilateral traingle of side 0.5m

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Solution

Dear Student,
work done on the system is change in their potential energies in the two configurations.
let q1= 1C
q2 = 2C
q3 = 3C
so initial potential energy of the arrangement r=1m
U = k (q1q2/r +q2q3/r + q3q1/r) where k is constant ( 9 * 10⁹)
= k(2+6+3)/1
U _initial= 11k ............. (1)
initial potential energy of the arrangement r=0.5 m
U_final = k (q1q2/r +q2q3/r + q3q1/r)
=k(2+6+3)/0.5
=22 k ........................ (2)

Work Done = U_final- U initial
= 22k - 11k
= 11 k
= 11 * 9*10⁹
= **99 * 10⁹ Joule** ans

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