Electrostatics – Page 2

Electric field from a sphere with a cavity

January 8th, 2022jeefirst0 Comments

A sphere of radius $a$ is filled with positive charge with uniform density $\rho$ . Then a smaller sphere of radius $a/2$ is carved out, as shown in the figure below, and left empty. What are the direction and magnitude of the electric field at $A$ ? At $B$ ?

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Solution

This problem can be solved by using the principle of superposition. For instance, consider a point charge $+q$ at some point $P$ in space. It creates an electric field everywhere. However, if you place a …

Flux from a charged shell

December 30th, 2021jeefirst0 Comments

JEE Advanced 2019 Paper 1, Question 8

A charged shell of radius $R$ carries a total charge $Q$ . Given $\Phi$ as the flux of electric field through a closed cylindrical surface of height $h$ , radius $r$
and with its center same as that of the shell. Here, the center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct?

[ $\epsilon_0$ is the permittivity of free space]

If $h > 2R$ and $r > R$ then $\Phi = Q/\epsilon_0$
If $h < 8R/5$ and $r = 3R/5$ then $\Phi = 0$
If $h > 2R$ and $r = 3R/5$ then $\Phi = Q/5\epsilon_0$
If $h > 2R$ and $r = 4R/5$ then $\Phi = Q/5\epsilon_0$

Related problems:
Electric field from a sphere …

Insulating spherical shell with a hole

December 30th, 2021jeefirst0 Comments

JEE Advanced 2019 Paper 1, Question 2.

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 $\alpha 4 \pi R^2 \ (\alpha \ll 1)$ is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

The potential at the center of the shell is reduced by $2 \alpha V_0$
The magnitude of the eletric field at the center of the shell is reduced by $\frac{\alpha V_0}{2 R}$
The ratio of the potential at the center of the shell to that of the point at $R/2$ from center towards

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