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 the figure (Figure 1)? Give your answer in component form. Assume that x-axis is horizontal and points to the right, and y-axis points upward. Express your answers using two significant figures separated by a comma. What is the magnitude of the electric field at the position indicated by the dot in the figure. Express your answer using two significant figures. What is the angle measured cw from the positive z-axis of the electric field at the position indicated by the dot in the figure. Express your answer using two significant figures.

Explanation / Answer

A)
let

q1 = 10 nc (top left)

q2 = 10 nc (top right)

q3 = -5 nc (lower left)

Ex =   k*q2/(0.05^2 + 0.03^2)*5/sqrt(5^2 + 3^2) ) + k*q3/0.05^2

= 9*10^9*10*10^-9/(0.05^2 + 0.03^2)*(5/sqrt(5^2 + 3^2)) + 9*10^9*5*10^-9/0.05^2

= 4.07*10^4 N/c

Ey = k*q2/(0.05^2 + 0.03^2)*3/sqrt(5^2 + 3^2) ) - k*q1/0.03^2

= 9*10^9*10*10^-9/(0.05^2 + 0.03^2)*(3/sqrt(5^2 + 3^2)) - 9*10^9*10*10^-9/0.03^2

= -8.64*10^4 N/c

B) E = sqrt(Ex^2 + Ey^2)

= sqrt(4.07^2 + 8.64^2)*10^4

= 9.55*10^4 N/c

C) theta = tan^-1(Ey/Ex)

= tan^-1(-8.64/4.07)

= 65 degrees below +x axis.
or 295 degrees with +x axis in counter clockwise direction.

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