Four point charges are at the corners of a square of side a as shown in the figu

Question

Four point charges are at the corners of a square of side a as shown in the figure below. Determine the magnitude and direction of the resultant electric force on q, with ke,q, and a left in symbolic form. (Let B = 3.5q and C = 2.5q. Let the +x-axis be pointing to the right.)

magnitude     direction     Four point charges are at the corners of a square of side a as shown in the figure below. Determine the magnitude and direction of the resultant electric force on q, with ke,q, and a left in symbolic form. (Let B = 3.5q and C = 2.5q. Let the +x-axis be pointing to the right.)

Explanation / Answer

The force acting on q by B (of upper left side) = (3.5q^2)/a^2 .... along +x axis == Fx (Say)
The force acting on q by B (of lower right side) = (3.5q^2)/a^2 .... along +y axis == Fy (Say)
The force acting on q by C = 2.5q^2/ (a*sqrt(2))^2 .... in the direction of 45deg to both x ==Fxy (Say)

resultant force of Fx and Fy on q = (Fx^2+Fy^2)^(1/2) = F1 (say)

Now, the total force on q is the resultant of F1 and Fxy, let it be F.

F = (F1^2 + Fxy^2 + 2*F1*Fxy*cos45deg) = ???

Do the simple numerical calculation. And, though the sign of the charges, ie. +ve or -ve is not specified, assuming +ve, ie. all repulsive forces, the direction of the force on q is along the diagonal Cq.

F = F1 (1,0) + F2 (1/v2, 1/v2) + F3 (0,1)

F = kq(3.5q)/a

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