Question

A straight rod of length L = 21.60 cm, carries a uniform charge density, A = 1.95 Times 10^-6 C/m. The rod is located along the y-axis from y_1 = 0.00 to y_2 = L Find the expression for the electric field along the y-axis, E_y, at a point P, What is the magnitude of the electric field at y_0 = 50.00 cm?

Answer 1

The charge is a rod of uniform charge distribution along Y-axis. The Gaussian surfaces will be co-axial cylinders with the said rod and the Electric field will be perpendicular to the Gaussian surfaces, i.e. along X-axis only. As such expression for electric field along Y does not exist.

If the rod is taken as a charge, which is concentrated at the centre of the rod, then the charge on the rod will be 195 x 0216 microcoulobs e.e. o.42336 $\mu C$ . This is once again centered at 10.8 cm from y=0, i.e. (50-10.8) = 39.2 cm becomes the actual distance. then the electric field at y=50 is got by the regular forula

$E=1/4\pi \varepsilon .(Q/r^2{})$

Substitution 9 x 10 (9) for $E=1/4\pi \epsilon$ and charge and distances, then the value of E becomes 2.78 x 10 (4) N /C

Then the point y = 50