A positive charge of 3.7 times 10^-9 C is brought in from infinity to a point (2

Question

A positive charge of 3.7 times 10^-9 C is brought in from infinity to a point (2m,0). How much work did the electric field do W = Now another positive charge of 3.7 times 10^-9 C is moved from infinity to the coordinates (1m, 2m). How much additional work was done by the electric field (The original charge is held in place. ) Finally, a negative charge of -3.7 times 10^-9 C is moved from infinity to the coordinates (-2m,0). How much additional work was by the electric field (The original two charges is held place.)

Explanation / Answer

there are no other charges present except +q,then Work done W = 0 J

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if another charge is at (1m,2m) then

W = -k*q1*q2/r = (-9*10^9*3.7^2*10^-18)/sqrt((2-1)^2+2^2) = -5.5*10^-8 J

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if another charge is -3.7*10^-9 C at (-2m,0)

then W = (-k*q^2)/r1 + (-k*q^2)/r2

W = ((-9*10^9*(3.7^2*10^-18))/sqrt((2-1)^2+2^2)) + ((-9*10^9*3.7^2*10^-18)/sqrt((-2-1)^2+(0-2)^2)) + ((-9*10^9*3.7^2*10^-18)/4) = -1.2*10^-7 J

So additional work done is (0.55*10^-7) - (1.2*10^-7) = 6.5*10^-8 J

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