An arc of radius $r$ carries charge. The linear density of charge is $\lambda$ and the arc subtends a angle $\frac{\pi }{3}$ at the centre. What is electric potential at the centre
$\frac{\lambda }{{4{\varepsilon _0}}}$
$\frac{\lambda }{{8{\varepsilon _0}}}$
$\frac{\lambda }{{12{\varepsilon _0}}}$
$\frac{\lambda }{{16{\varepsilon _0}}}$
Two insulated charged conducting spheres of radii $20\,cm$ and $15\,cm$ respectively and having an equal charge of $10\,C$ are connected by a copper wire and then they are separated. Then
Consider a sphere of radius $R$ having charge $q$ uniformly distributed inside it. At what minimum distance from its surface the electric potential is half of the electric potential at its centre?
Consider three concentric metallic spheres $A, B$ and $C$ of radii $a , b, c$, respectively where $a < b < c$. $A$ and $B$ are connected, whereas $C$ is grounded. The potential of the middle sphere $B$ is raised to $V$, then the charge on the sphere $C$ is
The variation of electrostatic potential with radial distance $r$ from the centre of a positively charged metallic thin shell of radius $R$ is given by the graph
A thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V _0$. A hole with a small area $\alpha 4 \pi R ^2(\alpha<<1)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?