Consider a dipole consisting of a charge of +3 microcoulombs located at y =+2 m

Question

Consider a dipole consisting of a charge of +3 microcoulombs located at y =+2 m and -3 microcoulombs located at y = -2 m.

31. What is the potential at x = 0, y = 4m?

ans = 9000 v

32. What is the E field at x = 0, y = 4m?

ans = 6000 v/m

33. If a third charge of +2 microcoulombs is placed at x = 0, y = 4m, what is the potential energy of this third charge as a result of the presence of the dipole?  

ans = 0.018 J

34. How much work must be done to bring such a +2 microcoulomb charge in from infinity to x =0, y=4m?

ans =0.018 J

35. What is the force on such a +2 microcoulomb charge when placed at x = 0, y = 4m?

Ans = 0.012 N

Explanation / Answer

31) V = k q1/r1 + k q2/r2 = 9E9*3.0E-6/2 + 9E9*-3.0E-6/6= 9000 V

32) E = k q1/r1^2 - k q2/r2^2 = 9E9*3.0E-6/2^2 + 9E9*-3.0E-6/6^2= 6000 V/m

33) PE = q V = 2.0E-6*9000 = 0.018 J

34) at infinity, PE = 0 so
W = dPE = 0.018 - 0 = 0.018 J

35) F = q E = 2.0E-6*6000 = 0.012 N

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