The figure shows three charges on the corners of a square with sides of length L

Question

The figure shows three charges on the corners of a square with sides of length L. The three charges have the relative values:

Q1 = Q, Q2 = 3.0 Q, Q3 = -2.0 Q

What is the direction of the total electric field at the fourth corner of the square?

Give your answer in degrees to at least 3 digits.

Give your angle counter-clockwise relative to the horizontal (x) axis. Use negative angles for directions below the x-axis (pointing in the negative y-direction). Your angles should be somewhere between -90 degrees and 90 degrees.

Explanation / Answer

Electric Field due to Charge Q1 = k*Q/L^2 i N/C

Electric Field due to Charge Q2 = k*3Q/(sqrt(2)* L)^2 * (L/sqrt(2)* L) i + k*3Q/(sqrt(2)* L)^2 *  (L/sqrt(2)* L)  N/C
Electric Field due to Charge Q2 = 3kQ/ 2L^2 * (1/sqrt(2)) i + 3kQ/ 2L^2 * (1/sqrt(2)) j N/C

Electric Field due to Charge Q3 =- k*2Q/L^2 j N/C

Net Electric Field = (k*Q/L^2 + 3kQ/ 2L^2 * (1/sqrt(2))) i +  (3kQ/ 2L^2 * (1/sqrt(2)) - 2kQ/L^2) j

Direction , tan() =  (3kQ/ 2L^2 * (1/sqrt(2)) - 2kQ/L^2) / (k*Q/L^2 + 3kQ/ 2L^2 * (1/sqrt(2)))
tan() = (3/(2*1.414) - 2)/(1 + 3/(2*1.414)
= tan^-1(0.455)
= - 24.470 Below Horizontal axis.

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