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 = 3.5 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

here,

Electric Field between two cahrges is given by

E = K*Q1*Q2 / R^2

so,
Electric force between q2 and q3

F23 = Fx = -2.0K*Q/L^2

Electric force between q2 and q1

F21 = Fy = 3.5K*Q/L^2

total electric field will be

as this is square the resulatnt will make 45 degree with horizontal x axis

F24 = Fxcos +FySin

length of F24 = sqrt(L^2 +L^2) = 1.41 L

F24 = (2.0*K*Q/L^2)*Cos45 + (3.5*K*Q/L^2)*Sin45

F24 = K*Q ( 1.414 / 1.414^2 + 2.474 / 1.414^2 )

F24 = 1.994 N/C

As tan = Fy/Fx = 3.5 / 2.0 = 1.75

is 60.255 degrees

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