Three point charges of `3 mu C, 4 mu C, and 5 mu C ` are arranged at the three corners of a right angled triangle ABC as shown in the figure. The work done in moving the charges at A and C, so that the three charges are located at the three corners of an equilateral triangle of side 3 cm is

Options

A. 0.3 J
B. 1.1 J
C. 2.2 J
D. 3.3 J

Answer

D

Explanation

According to question,

In a right angle triangle , in `Delta`ABC
`AC^(2) = AB^(2) + BC^(2)`
`rArr " " AC = sqrt( AB^(2) + BC^(2)) = sqrt( ( 4 xx 10^(-2))^(2) + (3 xx 10^(-2))^(2) )`
`rArr AC = 5 xx 10^(-2)` m
Initial electric potential energy of three charges,
U = `(k q_(1) q_(2))/(AB) + (k q_(1) q_(3))/(AC) + (k q_(2) q_(3))/(BC) `
= ` (k(4 xx 3 xx 10^(-12)))/(4 xx 10^(-2)) + (k( 4 xx 5 xx 10^(-12)))/( 5 xx 10^(-2)) + (k(3 xx 5 xx 10^(-12)))/(3 xx 10^(-2) ) `
=` k [ 3 xx 10^(-10) + 5 xx 10^(-10) ]`
` = 9 xx 10^(9) xx 12 xx 10^(-10)`
` = 108 xx 10^(-1) = 10.8 `J
When three charges located of an equilateral triangle of side 3 cm, the final potential energy of three charges system,
= `(kq_(1) q_(2))/( AB) + (k q_(2) q_(3))/( BC) + (k q_(1) q_(3))/(AC) `
` = (k (4 xx 3 xx 10^(-12) ))/( 3 xx 10^(-2)) + (k (3 xx 5 xx 10^(-12) ))/( 3 xx 10^(-2)) +(k (4 xx 5 xx 10^(-12) ))/( 3 xx 10^(-2)) `
` = (9 xx 10^(9))/(3) [ 12 xx 10^(-10) + 15 xx 10^(-10) + 20 xx 10^(-10) ] = 14.1 `J
Hence, the work done in moving charges at points. A and C, W = ( 14.1 - 10.8) = 3.3 J.