Charge q1 = 6.5 nC is loacted at the coordinate system origin, while charge q2 =

Question

Charge q1 = 6.5 nC is loacted at the coordinate system origin, while charge q2 = 1.7 nC is located at (a,0), where a = 1.4 m. The point P has coordinates (a,b), where b = 0.85 m. A third charge q3 = 3.5 nC will be placed later.

A) Find the electric potential Vp at point P, in volts. Assume the potential is zero at infinity.

B) How much work W, in joules, would you have to do to bring the third charge, q3, from very far away to the point P?

C) What is the total potential energy U, in joules, of the final configuration of three charges?

Explanation / Answer

A)Vp = V1+V2 =kq1/r1+kq2/r2= k(q1/sqrt(a^2+b^2)+q2/r2) = (9*10^9)*[(6.5*10^-9/sqrt(1.4^2+0.85^2))+1.7*10^-9/0.85] = 53.72 volt

B) W= q3*Vp = (3.5*10^-9)*(53.72) = 1.88*10^-9 J

C) U= k[q1q2/a+q1q3/sqrt(a^2+b^2) +q2q3/b^2] = (9*10^9)*[(6.5*10^-9*1.7*10^-9)/1.4 + (6.5*10^-9*3.5*10^-9)/ sqrt(1.4^2+0.85^2) + (1.7*10^-9*3.5*10^-9)/0.85] = 2.5*10-7 J

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