The charges shown are q 1 = 3.0 ?C (bottom left charge), and q 2 = 6.0 ?C. Charg

Question

The charges shown are q1 = 3.0 ?C (bottom left charge), and q2 = 6.0 ?C. Charge q3 = -3.0 ?C (not shown) is at infiniti. The distances are a =1.00cm, b =2.60cm, and c =1.70cm. The point labeled "X" is at the top left corner, a distance c away from q1 and a distance a away from the point labeled Y.  The point labeled "Y" is between charges q1 and q2, it is a distance a away from q1 and a distance b away from q2.

(a) With charges q1 and q2 in place, how much additional energy in Joules needs to be expanded to bring charge q3 to the point labeled "Y"?

(b) With charges q1 and q2 in place, how much additional energy in Joules needs to be expanded to instead bring charge q3 to the point labeled "X"?

(c) What if q3 was already brought to "X" how much energy in Joules needs to be expanded to move it to the point labeled "Y"?

Explanation / Answer

part a)

additional energy needed is

U1=kq1q3/a+kq2q3/b

where q1,q2,q3 are with their signs

part b)

U2=kq1q3/c+kq2q3(c2+(a+b)2)1/2

part c)

energy needed=U1-U2

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