Question

Consider a non-conducting rod of length $l$ having a uniform charge density $\lambda$ . Find the electric potential at $P$ , at a perpendicular distance $y$ above the midpoint of the rod.

• A. $\frac{\lambda }{2\pi {ϵ}_0}\ln \frac{l}{y}$
• B. $\frac{\lambda }{3\pi {ϵ}_0}\ln \frac{l}{y}$
• C. $\frac{\lambda }{4\pi {ϵ}_0}\ln \frac{l}{y}$
• D. $\frac{\lambda }{\pi {ϵ}_0}\ln \frac{l}{y}$

Answer 1

The correct option is A $\frac{\lambda }{2\pi {ϵ}_0}\ln \frac{l}{y}$

Charge density $=\lambda$

length $=l$

electric potential $=p$

perpendicular distance $=y$

The same procedure electric potential $=\frac{p}{{ϵ}_0}$

For non conducting rod of length

$E.2ds=\frac{\lambda ds}{ϵ}$

$E=\frac{6}{2{ϵ}_0}$

For inner and outer length from the mid point $\frac{\lambda }{2\pi {ϵ}_0}ln\frac{l}{y}$