Four equal charges q are placed at four corners of a square of side a each work done in carrying a charge -q from its centre to infinity
Answers
Answer:
At the center of the square as a result of the four equal charges q at the corners, potential(V) will be .
As, the sides are a thus the diagonals will be of length a√2, so both of the diagonals will be 2*a√2.
By using the formulae, V=4q/4πε0(a√2)2=√2qπε0a.
Since, work done from center O to infinity W0∞=−W∞0.
Work done(W) = −(−q)V=√2q^2/πε0a.
Answer:
√2q²/πea or 4√2 kq²/a
Explanation:
Workdone in moving a charge(q) from infinity to a certain point(at P.D. V) is qV.
Therefore,
Workdone in moving a charge(q) from a certain point(at P.D. V) to infinity is - qV.
Let the square be ABCD and centre be O. Since it is a square, AO = BO = CO = DO.
Work by q C charge = - qV = - q(k Q/r)
Work by 4 such charge = - 4kq(Q/r)
Substitute Q = - q, r = ½ diagonal = (a√2)/2
Total Workdone = - 4qk (-q/(a√2/2))
Total Workdone = 4kq² (2/a√2)
Total work = 4√2 kq²/a , where k = 1/4πe.
Work = √2q²/πea
*if charges are not same(say q and Q), you can simply substitute qQ instead of Q². *e refers to epsilon, here.