The balls on the figure charged to 2.2 nC . What are the strength and direction

Question

The balls on the figure charged to 2.2 nC . What are the strength and direction of the electric field at the position indicated by the dot in the figure (Figure 1)? You may want to review (pages 752 - 756) . For help with math skills, you may want to review: Vector Addition For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Charge on a Van De Graaff. Part A Specify the strength of the electric field. Express your answer using two significant figures. Part B Specify the direction. Express your answer using two significant figures.

Explanation / Answer

E = kq/r^2

At the dot:
r1 = 5cm = 0.05m
so E1 = 9x 10^9 x 2.2 x 10^-9 / (0.05)^2 = 7920 N/C
E1 = 7920 N/C in +x direction

for vertical ball

r2 = sqrt(5^2 + 10^2) cm = 11.18 cm = 0.112 m

so E2 = 9x10^9 x 2.2 x 10^-9 / (0.112)^2 = 1578.44 N/C

Angle is 90 - arctan(5/10) = 63.43 deg

E2 = in x direction = E2costheta = 1578.44 cos63.43 = 706.02 N/C

in y direction = E2sintheta = 1411.74 N/C

Extotal = 706.02 + 7920 = 8626.02 N/C

Ey = 1411.74

E = sqrt(Extota^2 + Eytotal^2)

E = 8740.78 N/C = 8.7 x 10^3 N/C

direction = Ey/Ex = tantheta

theta = tan^-1(Ey/Ex)

theta = tan^-1(1411.74/8626.02)

theta = 9.3 degree

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