Question

The magnitude of electric field at distance $r$ from an infinitely thin rod having a linear charge density $\lambda$ is ?

Answer 1

Consider a long straight wire carrying a uniform charge per unit length$\lambda$.

Let the Gaussian surface be a cylinder as the field generated by this charge carrying wire will be radially outward, uniform and symmetrical.

Thus according to the gauss law the electric field at the distance.$r$.from the wire is given as

$\varphi ={\iint }_{s}E\cdot ds$

$\varphi =\frac{\lambda L}{{\in }_0}$

$dA$is the infinitesimal surface element$=2\pi rL$

Now Substituting the values in the above formula, we get

$E=\frac{\lambda }{2\pi {\in }_{0}r}$