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Find the potential at the centre of a sq...

Find the potential at the centre of a square of side `sqrt(2)m` which carries at its four corners charges `+2 xx 10^(-9)C, +1 xx 10^(-9)C, -2 xx 10^(-9)C` and `+3 xx 10^(-9)C`.

Text Solution

Verified by Experts

`AB = sqrt(2)m = BC`

`:. AC = sqrt(AB^(2)+BC^(2)) = sqrt((sqrt2)^(2)+(sqrt2)^(2)) = 2m = BD`
`:. AO = BO = CO = DO = 1m`
`:. V_(O) = 1/(4piepsilon_0)((q_1)/(AO) + (q_2)/(BO) + (q_3)/(CO) + (q_4)/(DO))`
` = 9 xx 10^(9) xx ((2xx10^(-9))/(1) + (1xx10^(-9))/(1) - (2xx10^(-9))/(1) + (3xx10^(-9))/(1))`
` = 9 xx (2 + 1 - 2 + 3) = 36V`.
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