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 Give your answer in component form. (Assume that x-axis is horizontal and points to the right, and y-axis points upward) Express your answer in terms of the unit vectors i and j. Express your answer using two significant figures. Give your answer as a magnitude and angle measured cw from the positive x·axis. Express your answer using two significant figures. Express your answer using two significant figures.

Explanation / Answer

E1x= 0 N/C

E1y= kq1/r1^2 = (9*10^9*5*10^-9)/0.04^2 = 28125 N/C j^

E2= kq2/r2^2 = (9*10^9*10*10^-9)/(sqrt(0.02^2+0.04^2)^2 = 45000 N/C

= tan^-1(0.04/0.02) = 63.43 deg

E2x = E2cos63.43 = 45000cos63.43 = 20128.1 N/C i^

E2y = E2sin63.43 = 45000sin63.43 = -40247.5 N/C j^

E3x= kq3/r3^2 = (9*10^9*5*10^-9)/0.02^2 = 112500 N/C i^

E3y = 0 N/C

Enetx= E1x + E2x + E3x = 0 +20128.1 + 112500 = 132628.1 N/C

Enety= 28125 -40247.5 + 0 = -12122.5 N/C

A) E = 132628.1 i^ -12122.5 j^

B) |E| = sqrt(132628.1^2 + 12122.5^2) = 1.3*10^5 N/C

C) = tan^-1(-12122.5/132628.1) = -5.22 deg

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