Two charges are arranged as shown on the right. Charge q_1 = -48 pC is placed on

Question

Two charges are arranged as shown on the right. Charge q_1 = -48 pC is placed on the positive y-axis at y = 4.0 cm. Charge q_2 = -100 pC is placed on the positive x-axis at x = 5.0 cm. a) Calculate the magnitude and direction of E_1, the electric field at the origin due to q_1. b) Calculate the magnitude and direction of E_2, the electric field at the origin due to q_2. c) Calculate the x-component as well as the y-component of E, the total electric field at the origin. d) Calculate the magnitude and direction of E. e) A charge q_3 = 20 pC is placed on the origin. Calculate the magnitude and direction of force F on

Explanation / Answer

Given

q1 = -48 pC

r1 = 4.0 cm

q2 = -100 pC

r2 = 5.0 cm

a) E1 = kq1/r1^2 = (9*10^9*48*10^-12)/0.04^2 = 270 N/C (Along +y-axis)

b) E2 = kq2/r2^2 = (9*10^9*100*10^-12)/0.05^2 = 360 N/C (Along +x-axis)

c) x-component of E = Ex = 360 N/C

    y-component of E = Ey = 270 N/C

d) Total electric field = E = sqrt[360^2 + 270^2] = 450 N/C

    Direction = arctan(270/360) = 36.9 degree

e) Force = qE = 20*10^-12*450 = 9 nN   along 36.9 degree with +x-axis.

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