Four positive point charges +q are kept at the four corners of a square of side l. The net electric field at the mid-point of any one side of the square is (Take, `(1)/(4pi epsi_(0)) = k`)

Options

A. `(4kq)/(l^(2))`
B. `(16kq)/(5 sqrt5l^(2))`
C. `(8kq)/(sqrt5l^(2))`
D. `(kq)/(l^(2))`

Answer

B

Explanation

The force at midpoint of any side of a square let.s say at point P which is midpoint of side AB is due to charges at corners A, B, C and D
`F_(P) = F_(AP) + F_(BP) + F_(CP) + F_(DP)`

AP = DP = l
`BP = CP = sqrt(l^(2) + (1//2)^(2)) = sqrt(5l^(2)//4)`
Electric field due to charges at A and D will be equal in magnitude and opposite in direction, so will cancel each other.
Similarly, the vertical components of electric field due to charges at B and C will also cancel each other, but hte horizontal components of these will add up to give resultant electric field.
`E = 2.(kq)/((sqrt(5l^(2)//4))^(2)).cos theta = 2 xx (4kq)/(5l^(2)) xx (2)/(5) = (16 kq)/(5sqrt5l^(2))`