Three points charges of `1 C, 2C and 3C` are placed at the corners of an equilateral triangle of side 100 cm. Find the work done to move these charges to the corners of a similar equilateral triangle of side 50 cm.

Options

A. `3.3 xx 10^(10) J`
B. `6.6 xx 10^(10) J`
C. `9.9 xx 10^(10) J`
D. zero

Answer

3

Explanation

`U_(1) = (1)/(4 pi in_(0)) [ (1 xx 2)/(1) + ( 2 xx 3)/(1) + ( 3 xx 1)/(1)] = (11)/( 4 pi in_(0))`
`U_(2) = (1)/(4 pi in_(0)) [ (1 xx 2)/(0.5) + (2 xx 3)/(0.5) + ( 3 xx 1)/(0.5)] = (22)/(4 pi in_(0))`
`W_(1 rarr 2) = U_(2) - U_(1) = (11)/(4 pi in_(0))`
`= 9 xx 10^(9) xx 11 = 9.9 xx 10^(10) J`