A charge Q is uniformly distributed over a ro | vedclass

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

Question

(D) The linear charge density of the rod is $\lambda = \frac{Q}{L}$.Consider a small element of length $dx$ at a distance $x$ from point $O$.The charg

Vedclass · Accepted Answer

$\frac{Q \ln 2}{4\pi \epsilon_0 L}$

Vedclass · Answer

(D) The linear charge density of the rod is $\lambda = \frac{Q}{L}$.Consider a small element of length $dx$ at a distance $x$ from point $O$.The charge of this element is $dq = \lambda dx = \frac{Q}{L} dx$.The potential $dV$ at point $O$ due to this element is $dV = \frac{k dq}{x} = \frac{1}{4\pi \epsilon_0} \frac{Q}{L} \frac{dx}{x}$.To find the total potential $V$,integrate from $x = L$ to $x = 2L$:$V = \int_{L}^{2L} \frac{Q}{4\pi \epsilon_0 L} \frac{dx}{x} = \frac{Q}{4\pi \epsilon_0 L} [\ln x]_{L}^{2L}$.$V = \frac{Q}{4\pi \epsilon_0 L} (\ln 2L - \ln L) = \frac{Q}{4\pi \epsilon_0 L} \ln\left(\frac{2L}{L}\right) = \frac{Q \ln 2}{4\pi \epsilon_0 L}$.

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

Similar Questions

If $4 \times 10^{20} \text{ eV}$ of energy is required to move a charge of $0.25 \text{ C}$ between two points,what will be the potential difference between them in volts?

An electric charge $10^{-8} \ C$ is placed at the point $(4 \ m, 7 \ m, 2 \ m)$. At the point $(1 \ m, 3 \ m, 2 \ m)$,the electric

If identical charges $(-q)$ are placed at each corner of a cube of side $b$,then the electric potential energy of charge $(+q)$ which is placed at the center of the cube will be:

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:

$A$ point charge $q$ is surrounded by eight identical charges,each of magnitude $q$,at a distance $r$ as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge at the center is moved to infinity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module