Question

In the figure two curved plastic rods, one of charge +q and the other of charge -q, form a circle of radius R = 8.25 cm in an xy plane. The x axis passes through both of the connecting points, and the charge is distributed uniformly on both rods. If q = 13.6 pC, what is the magnitude of the electric field produced at P, the center of the circle?

+9 -q

Answer 1

The Net Electric field at center of the circle due to curved rod of charge q is:

$E_{net}=\frac{2k\lambda }{R}$ downward

Charge density

$\lambda =\frac{Q}{\pi R}=\frac{13.6\times 10^{-12}}{\pi \times 0.0825}=5.24\times 10^{-11}C/m$

So net electric field at center of the circle is the sum of both fields (they both go downward)

$E_{net}=\frac{4k\lambda }{R}$

$E=\frac{4\cdot 9\cdot 10^{9}\cdot 5.24\times 10^{-11}}{0.0825}$