Three point charges 3 nC , 6 nC and 9 nC are placed at the corners of an equilateral triangle of side `0.1` m . The potential energy of the system is

Options

A. 89100 J
B. 99100 J
C. 8910 J
D. 9910 J

Explanation

The potential energy of the system of three charges is
` U = 1/(4piepsilon_(0)) [ (q_(1)q_(2))/(r_(12)) + (q_(1)q_(3))/(r_13) = (q_(2)q_(3))/(r_(23))] `
Here ,
` q_(1) = 3 nC = 3xx 10^(-9) C `
` q_(2) = 6 nC = 6 xx 10^(-9) C `
`q_(3) 9 nC = 9 xx 10^(-9) C `
` r_(12) = r_(13) = r_(23) = 0.1 m `

` . U = (9xx10^(9) "N m"^(2)C^(-2))[ ((3xx10^(-9)C)(6xx10^(-9)C))/0.1+ ((3xx10^(-9)C)(9xx10^(-9)C))/(0.1 m) + ((6xx10^(-9)C)(9xx10^(-9)C))/(0.1)] `
` U = ((9xx10^(9)" Nm"^(2)C^(-2)))/((0.1m)) [ (18xx10^(-18)C^(2)) + (27 xx10^(-18) C^(2))+ (54 xx10^(-18)C^(2)) ] `
`= ((9xx10^(9)"N m"C^(-2))(99xx10^(-18)C^(2)))/((0.1m))`
` = 8910 xx 10^(-9) J ` .