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

$E = \frac{2k\lambda sin\frac{\theta}{2}}{R}$

here we know that

$\lambda = 5nC/m$

$k = 9 \times 10^9 Nm^2/C^2$

$\frac{\pi}{2}R = L = 2m$

$R = \frac{4}{\pi}$

also we know that

$\theta = \frac{\pi}{2}$

now from above formula

$E = \frac{2(9\times 10^{-9})(5\times 10^{-9})sin45}{4/\pi}$

$E = 50 N/C$