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

No current flows between two charged bodies connected together when they have the same

Three concentric metallic spherical shells $A, B,$ and $C$ of radii $a, b,$ and $c$ $(a < b < c)$ have surface charge densities $-\sigma, +\sigma,$ and $-\sigma$ respectively. The potential of shell $A$ is:

$A$ thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is:

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ $(r > a)$ is ($\varepsilon_0$ is the permittivity of free space):

The potential at a point,due to a positive charge of $100\,\mu C$ at a distance of $9\,m$,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module