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 3.71 Q, Q3 -1.22 Q Q is some (arbitrary) positive charge. 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 axis. Use negative angles for directions below the x-axis (pointing in the negative y-direction). Your angles will be somewhere between -90 degrees and 90 degrees to the horizontal (k) Q2 Q3

Explanation / Answer

from the given data

|E1| = k*Q1/L^2

= k*Q/L^2 N/C (towards +x axis)

|E2| = k*Q2/(2*L^2)

= k*3.71*Q/(2*L^2)

= 1.855*k*Q/L^2 N/C (45 degrees above +x axis)

|E3| = k*Q3/L^2

= k*1.22*Q/L^2

= 1.22*k*Q/L^2 (towards -y axis)

x-component of net electric field,
Enetx = E1x + E2x + E3x

= k*Q/L^2 + (1.855*k*Q/L^2)*cos(45) + 0

= 2.31*k*Q/L^2

y-component of net electric field,
Enety = E1y + E2y + E3y

= 0 + (1.855*k*Q/L^2)*sin(45) - 1.22*k*Q/L^2

= 0.0917*k*Q/L^2

angle made by net electric field with +x axis,

theta = tan^-1(Enety/Enetx)

= tan^-1(0.0917/2.31)

= 2.27 degrees <<<<<<<<---------------------Answer

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