Calculate the magnitude of the electric field at one corner of a square 2.12 m o

Question

Calculate the magnitude of the electric field at one corner of a square 2.12 m on a side if the other three corners are occupied by 4.75×106 C charges. Express your answer to three significant figures and include the appropriate units.

What is the direction of the electric field at the corner?

What is the direction of the electric field at the corner?

along the side of the square between the corner and one of the charges toward the charge along the side of the square between the corner and one of the charges outward of the charge along the line between the corner and the center of the square toward the center along the line between the corner and the center of the square outward of the center

Explanation / Answer

Electric field is defined as the force experienced by a unit positive charge. Suppose a square ABCD is given where the charges are at B, C and D and electric field is to be worked out at A.

Electric field due to the charge B and D would be equal in magnitude = kq/r^2

= (9x10^9) * (4.75 x 10^-6) / (2.12)^2 N/C = 9511.84 N/C

The resultant of two such charges will be along CA
= 2cos45° * [9511.84] N/C

= 13451.76 N/C

Electric field due to charge at C will be along CA = kq/(2r)^2

        = (9x10^9) * (4.75 x 10^-6) / (2.122)^2

                                                                                = 4756 N

Total field = 13451.76 + 4755.9 = 18207.7 N/C in the direction CA.

Direction is along the side of the square between the corner and one of the charges toward the charge

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