Two spheres, one with charge Q_1 = 3 times 10^-9 C and the other with charge Q_2

Question

Two spheres, one with charge Q_1 = 3 times 10^-9 C and the other with charge Q_2 = -4 times 10^-9 C are located 3m apart, as shown in the figure below. Point A is 1m from Q_1 and 4m from Q_2, and point B is 2m from Q_1 and 3. 61m from Q_2. The angles A-Q_1-B and B-Q_1-Q_2 are right angles, and the angle Q_1-Q_2-B is 33. 7degree. a) What is the potential difference between points A and B? b) What is the electric field at point A and at point B? (Give your answer as either a magnitude and direction or in terms of x and y components)

Explanation / Answer

q1 = 3 * 10^-9 C
q2 = -4 * 10^-9 C

(a)
Potential At point A, Va = k*q1/r1 + k*q2/r2
Potential At point A, Va = (8.9*3)/1 - (8.9*4)/4
Potential At point A, Va = 17.8 V

Potential At point B, Vb = k*q1/r1 + k*q2/r2
Potential At point B, Vb = (8.9*3)/2 - (8.9*4)/3.61
Potential At point B, Vb = 3.49 V

Potential Difference btw Point A & B = 17.8 - 3.49
Potential Difference btw Point A & B = 14.31 V

(b)
Electric Field at Point A, Ea = [- k*q1/r1^2 + k*q2/r2^2] i^
Electric Field at Point A, Ea = [- (8.9*3)/1^2 + (8.9*4)/4^2 ] i^
Electric Field at Point A, Ea = - 24.475 i^ N/C   

Electric Field at Point B, Eb = [ - k*q1/r1^2 j^ ] + [ k*q2/r2^2 * cos(33.7) i^ + k*q2/r2^2 * sin(33.7) j^]
Electric Field at Point B, Eb = (- (8.9*3)/2^2 + (8.9*4)/3.61^2) * sin(33.7) j^ +  (8.9*4)/3.61^2) * cos(33.7) i^
Electric Field at Point B, Eb = 2.27 i^ - 5.16 j^ N/C

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