Question

A uniformly charged rod (length = 2.0 m, charge per unit length = 5.0 nc/m) is bent to form one quadrant of a circle. what is the magnitude of the electric field at the center of the circle?

Answer 1

Electric field at the center of circular arc is given by the formula

`E = (2k\lambda sin(\theta)/(2))/(R)`

here we know that

`\lambda = 5nC/m`

`k = 9 * 10^9 Nm^2/C^2`

`(\pi)/(2)R = L = 2m`

`R = (4)/(\pi)`

also we know that

`\theta = (\pi)/(2)`

now from above formula

`E = (2(9* 10^(-9))(5* 10^(-9))sin45)/(4/\pi)`

`E = 50 N/C`