In the figure, four charges, given in multiples of 7.00×10-6 C form the corners

Question

In the figure, four charges, given in multiples of 7.00×10-6 C form the corners of a square and four more charges lie at the midpoints of the sides of the square. The distance between adjacent charges on the perimeter of the square is d = 1.20×10-2 m.

What are the magnitude and direction of the electric field at the center of the square? The magnitude of E?

What is the X component of the electric field (Ex) at the center of the square?

What is the Y component of the electric field (Ey) at the center of the square?

Explanation / Answer

For finding electric field at center, we can cancel charges on opposite ends having equal magnitude

so we are left with -10q in top right corner and -3q in right (x direction)

Ex = sigma kq/r^2 = 9*10^9*7*10^-6* [ (10/(1.41*0.012)^2) * 0.707 + 3/0.012^2]

= 2.868 *10^9 N/C

Ey = sigma kq/r^2 = 9*10^9*7*10^-6* [ (10/(1.41*0.012)^2) * 0.707 ]

=1.556 *10^9 N/C

Magnitude of E = sqrt{Ex^2 + Ey^2} = 3.263 *10^9 N/C

direction =arctan (1.556/2.868) = 28.48 degree

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