What are the strength and direction of the electric field at the position indica

Question

What are the strength and direction of the electric field at the position indicated by the dot in figure?

Part A)

Give your answer in terms of the horizontal and vertical components. Take the positive directions to be up and to the right.

Express your answer using two significant figures. Enter your answers numerically separated by a comma.

Ex, Ey = ________________ N/C

Part B)

Give your answer as a magnitude and angle measured from the positive x-axis.

Express your answer using two significant figures.

E = _____________________ N/C

Part C

Express your answer using three significant figures.

theta = __________________ clockwise from the +x-axis

Explanation / Answer

Part A)

Apply E = kq/r2 for each charge

For the 10nC to the right

E = (9 X 109)(10 X 10-9)/(.04)2

E = 56250 N/C to the left

For the 10 nC in the lower corner, the distance is from the Pyhthagorean Theorem...

r2 = (.04)2 + (.02)2 = .002

The angle is from the tangent function

Tan(angle) = .02/.04

Angle = 26.6o

E = (9 X 109)(10 X 10-9)/(.002)

E = 45000

Ex = 45000(cos 26.6) = 40237 N/C to the left

Ey = 45000(sin 26.6) = 20149 N/C up

For the -5nC at the bottom

E = (9 X 109)(5 X 10-9)/(.02)2

E = 112500 Downward

The net x = 56250 + 40237

Net x = 96487 N/C to the left

Using two sig figs. Ex = 9.6 X 104 N/C left

The net y = 112500 - 20149

Net y = 92351 Downward

Using two sig figs, Ey = 9.2 X 104 N/C Downward

Part B)

Net value is from the Pythagorean Theorem

Net2 = 923512 + 964872

Net = 133560 N/C

Using two sig figs, that is 1.3 X 105 N/C

Part C)

The angle from the tangent formula...

tan(angle) = 92351/96487

Using three sig figs, angle = 224o

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