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Four point charges each of charge -4muC ...

Four point charges each of charge `-4muC ` are placed at the four corners of a square such that they are in equilibrium when a charge q is placed at its centre. Find q.

Text Solution

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Suppose the side of square is a.
` F_1 = F_2 = (1)/(4 piin _0) . (16)/(2)`
` F = sqrt(F_1+F_2) = (1)/(4piin_0) . (sqrt2xx 16)/(2a^(2))`
` F_4 = (1)/(4 pi in_0) . =(-4q)/(4piin_0((a)/(2))^(2))= (-1)/(4piin_0) . (8q)/(a^(2))`
For equilibrium condition
` F + F_3 + F_4= 0 `
`(1)/(4piin_0) . (16 sqrt2)/(a^(2))+ (1)/(4piin_0) . (16)/(2a^(2)) - (1)/(4piin_0) . (8q)/(a^(2)) = 0 `
` 16 sqrt2+8-8q=0`
` " " 8q = 30.62`
` " " q= 3.82 muC `
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