A positive point charge q is placed at a dist | vedclass

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

Question

(B) Inside a metallic conductor,the net electric field must be zero in electrostatic equilibrium.Let $\vec{E}_{ext}$ be the electric field at the cent

Vedclass · Accepted Answer

$\frac{1}{4 \pi \varepsilon_0} \frac{q}{9 R^2}$

Vedclass · Answer

(B) Inside a metallic conductor,the net electric field must be zero in electrostatic equilibrium.Let $\vec{E}_{ext}$ be the electric field at the centre of the shell due to the external point charge $q$.Let $\vec{E}_{ind}$ be the electric field at the centre of the shell due to the induced charges on the surface of the shell.Since the net electric field at the centre is zero,we have $\vec{E}_{ext} + \vec{E}_{ind} = 0$,which implies $\vec{E}_{ind} = -\vec{E}_{ext}$.The magnitude of the electric field due to the point charge $q$ at the centre of the shell (which is at a distance $R + 2R = 3R$ from the charge) is given by $E_{ext} = \frac{1}{4 \pi \varepsilon_0} \frac{q}{(3R)^2} = \frac{1}{4 \pi \varepsilon_0} \frac{q}{9R^2}$.Therefore,the magnitude of the electric field due to the induced charge is $|\vec{E}_{ind}| = |\vec{E}_{ext}| = \frac{1}{4 \pi \varepsilon_0} \frac{q}{9R^2}$.

$A$ positive point charge $q$ is placed at a distance $2R$ from the surface of a metallic shell of radius $R$. The electric field at the centre of the shell due to the induced charge has a magnitude of:

Similar Questions

Two charged metallic spheres are joined by a very thin metal wire. If the radius of the larger sphere is four times that of the smaller sphere,the electric field near the larger sphere is

The radii of two metallic spheres $A$ and $B$ are ${r_1}$ and ${r_2}$ respectively $({r_1} > {r_2})$. They are connected by a thin wire and the system is given a certain charge. The charge will be greater:

‘The interior of a conductor can have no excess charge in the static situation’. Explain.

Write important results regarding the electrostatics of conductors.

Explain the construction of a Van de Graaff generator with a diagram and describe its uses.

Vedclass Test Series

Exam Paper Generator

Online Exam Module