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Positive charges of magnitude 6nC, 12 nC...

Positive charges of magnitude 6nC, 12 nC, and 24 nC are placed at the vertices, A, B and C of a square ABCD of side 20 cm. What is the amount of work done to place a charge of 1C at vertex D?

Text Solution

Verified by Experts

The length of diagonal `BD = sqrt(20^(2)+20^(2)) = 20sqrt(2)cm`
The electric potential at D,
`V_(D) = 1/(4pi epsilon_0) [(q_A)/(AD) + (q_C)/(CD) + (q_B)/(BD)]`
`1/(4 pi epsilon_0) [(6xx10^(-9))/(20xx10^(-2))+(24xx10^(-9))/(20xx10^(-2))+(12xx10^(-9))/(20sqrt(2)xx10^(-2))]`
`9 xx 10^(9) xx (10^(-9))/(10^(-2))[6/20 + 24/20 + (12sqrt2)/40]`
`=900[(12+48+12xx1.414)/(40)] = 45/2 xx 76.968`
`= 1731. 78 V`

Hence the work done to place a charge of 1C at D = 1731.78 J`.
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