A charge Q is uniformly distributed over a lo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the linear charge density of the rod be $\lambda = \frac{Q}{L}$.Consider a small element of length $dx$ on the rod at a distance $x$ from poin

Vedclass · Accepted Answer

$\frac{Q \ln 2}{4 \pi \varepsilon_0 L}$

Vedclass · Answer

(A) Let the linear charge density of the rod be $\lambda = \frac{Q}{L}$.Consider a small element of length $dx$ on the rod at a distance $x$ from point $O$.The charge on this element is $dq = \lambda dx = \frac{Q}{L} dx$.The electric potential $dV$ at point $O$ due to this element is given by $dV = \frac{1}{4 \pi \varepsilon_0} \frac{dq}{x} = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{L} \frac{dx}{x}$.The total potential $V$ at point $O$ is obtained by integrating from $x = L$ (at end $A$) to $x = 2L$ (at end $B$):$V = \int_{L}^{2L} \frac{Q}{4 \pi \varepsilon_0 L} \frac{dx}{x} = \frac{Q}{4 \pi \varepsilon_0 L} [\ln x]_{L}^{2L} = \frac{Q}{4 \pi \varepsilon_0 L} (\ln 2L - \ln L) = \frac{Q \ln 2}{4 \pi \varepsilon_0 L}$.

$A$ charge $Q$ is uniformly distributed over a long rod $AB$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at a distance $L$ from the end $A$ is

Similar Questions

Choose the $CORRECT$ option.

Charges of $2 \mu C$ and $-3 \mu C$ are placed at two points $A$ and $B$ separated by a distance of $1 \ m$. The distance of the point from $A$ where the net potential is zero is: (in $m$)

$A$ total charge $Q$ is distributed between two concentric spherical shells of radii $r$ and $R$ $(R > r)$ such that their surface charge densities are equal. What is the electric potential at their common center?

The maximum electric field that can be held in air without producing ionization of air is $10^7\,V/m$. The maximum potential,therefore,to which a conducting sphere of radius $0.10\,m$ can be charged in air is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module