Four charged particles are at the corners of a square of side a as shown in the

Question

Four charged particles are at the corners of a square of side a as shown in the figure below. (Let A = 4, B = 4, and C = 5.)

magnitude                          
direction         Four charged particles are at the corners of a square of side a as shown in the figure below. (Let A = 4, B = 4, and C = 5.) Determine the electric field at the location of charge q. (Use the following as necessary: q, a, and ke.) Determine the total electric force exerted on q. (Use the following as necessary: q, a, and ke.)

Explanation / Answer

(a) The electric field at charge q will be the sum of the electric fields caused by Aq, Bq and Cq.

For Aq E = ke*4q/a^2 at ang = 0 deg (x-axis)
For Bq E = ke*4q/(2a^2) at ang = 45 deg
For Cq E = ke*5q/a^2 at ang = 90 deg

The sum of these is Eq = ke*q*(1/a^2)*(4x + (2^0.5x + 2^0.5y) + 5y)

= ke*q*(1/a^2)*(5.414x + 6.414y)

= ke*q*(1/a^2)*(8.39) at ang = 49.8 deg

(b) The total electric force on q is simply Eq x q = ke*q^2*(1/a^2)*(8.39) at ang = 49.8 deg

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