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Charges +2 xx 10^(-7)C, -4 xx 10^(-7)C a...

Charges `+2 xx 10^(-7)C, -4 xx 10^(-7)C and +8 xx 10^(-7)C` are placed at the vertices of an equilateral triangle of side 10 cm in air. Determine the electrical potential energy of this system of charges.

Text Solution

Verified by Experts

Distance between any two of the charges, `r = 10 cm = 0.1 m`.
The electrical potential energy of the system of charges is the algebraic sum of the potential energies of each pair of the charges. For air, permittivity is `epsilon_(0)`.
`=1/(4 pi epsilon_0)((q_(1)q_(2))/r + (q_(2)q_(3))/r + (q_(3)q_(1))/r)`
`=1/(4 pi epsilon_0)(q_(1)q_(2) + q_(2)q_(3)+ q_(3)q_(1))`
`1/(4 pi epsilon_(0) xx 0.1) [2 xx (-4) +(-4) xx 8 + 8 xx 2] xx 10^(-7)`
`=(9 xx 10^(9))/(0.1) xx [-8 xx 10^(-14)-32xx10^(-14)+16xx10^(-14)]`
`= -(9xx24xx10^(9)xx10^(-14))/(0.1) = -0.0216 J`
The negative sign indicates that 0.0216J work is to be done to transfer the charges from their positions to infinity.
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