A square loop of side 'l' each side having uniform linear charge density 'lambda' is placed in 'xy' lane as shown in the figure There exists a non uniform electric field `vec(E)=a/l(x+l)hat(i)` where a and l are constants and x is the position of the point from origin along x-axis. Find the resultant electric force on the loop (in Newtons) if `l=10 cm lambda=20 muC//m and a=5 xx 10^(5) N//C`.

Answer

`6N`

Explanation

`F_(AB)=a/l(0+l)xxlambdal = a lambdal rightarrow
`F_(CD) = a/l (l+l)xxlambdal = 2alambdal`
For `F(AD) = F_(BC)`
`F= int a/l (x+l) lambda dx = (a lambda)/l[x^(2)/2+lx]_(0)^(l)=3/2a lambdal`
`6a lambdal=6xx5xx10^(5)xx20xx10^(-6)xx0.1`
`=6N`