In the figure, four charges, given in multiples of 6.0010 -6 C form the corners

Question

In the figure, four charges, given in multiples of 6.0010-6 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 = 7.1010-2 m. What are the magnitude and direction of the electric field at the center of the square? The magnitude of E?
Ex?


Ey?

In the figure, four charges, given in multiples of 6.00 times 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 = 7.10 times 10-2 m. What are the magnitude and direction of the electric field at the center of the square? The magnitude of E? Ex? Ey?

Explanation / Answer

Numbering the charges from top right from 1 to 8:

field due to charge 1 and 5 will cancel each other
field due to charge 2 and 6 will cancel each other
field due to charge 3 and 7 will add up and will be towards charge 3
field = 2 x 5kq/(d?2)2 = 5Kq/d2 at 45 degree from x axis


field due to charge 4 and 8 will add up and will be towards 4

field = 3kq/d2 along x axis

so,

Ex = Kq(5/?2 + 3)/d2 = 90x 106 N/C

Ey = 5Kq/?2d2 = 32.2 x 106 N/C

magnitude = 95.558 x 106 N/C

direction is at 19.68 degrees from x axis

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