$(a)$ A conductor $A$ with a cavity as shown in Figure $(a)$ is given a charge $Q$. Show that the entire charge must appear on the outer surface of the conductor.
$(b)$ Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A \text { is } Q+q$ [Figure $(b)$]
$(c)\;A$ sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
$(a)$ A conductor $A$ with a cavity as shown in Figure $(a)$ is given a charge $Q$. Show that the entire charge must appear on the outer surface of the conductor.
$(b)$ Another conductor $B$ with charge $q$ is inserted into the cavity keeping $B$ insulated from $A$. Show that the total charge on the outside surface of $A \text { is } Q+q$ [Figure $(b)$]
$(c)\;A$ sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
$(a)$ Let us consider a Gaussian surface that is lying wholly within a conductor and enclosing the cavity. The electric field intensity $E$ inside the charged conductor is zero. Let $q$ is the charge inside the conductor and is $\epsilon_{0}$ the permittivity of free space. According to Gauss's law, Flux,
$\phi=E . d s=\frac{q}{\epsilon_{0}}$
Here, $E =0 \Rightarrow \frac{q}{\epsilon_{0}}=0 \Rightarrow q=0$
$\left[\text { as } \epsilon_{0} \neq 0\right]$
Therefore, charge inside the conductor is zero. The entire charge $Q$ appears on the outer surface of the conductor.
$(b)$ The outer surface of conductor $A$ has a charge of amount $Q$. Another conductor $B$ having charge $+ q$ is kept inside conductor $A$ and it is insulated from $A$. Hence, a charge of amount $- q$ will be induced in the inner surface of conductor $A$ and $+q$ is induced on the outer surface of conductor $A$. Therefore, total charge on the outer surface of conductor $A$ is $Q+q$
$(c)$ A sensitive instrument can be shielded from the strong electrostatic field in its environment by enclosing it fully inside a metallic surface. A closed metallic body acts as an electrostatic shield.
Similar Questions
Given below are two statements.
Statement $I$ : Electric potential is constant within and at the surface of each conductor.
Statement $II$ : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options give below.
Given below are two statements.
Statement $I$ : Electric potential is constant within and at the surface of each conductor.
Statement $II$ : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options give below.
- [JEE MAIN 2022]
Two isolated metallic solid spheres of radii $R$ and $2 R$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$. The ratio $\frac{\sigma^{\prime}}{\sigma}$ is
Two isolated metallic solid spheres of radii $R$ and $2 R$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$. The ratio $\frac{\sigma^{\prime}}{\sigma}$ is
- [JEE MAIN 2023]
Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+ Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.
Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+ Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.
Assertion : A metallic shield in form of a hollow shell may be built to block an electric field.
Reason : In a hollow spherical shield, the electric field inside it is zero at every point.
Assertion : A metallic shield in form of a hollow shell may be built to block an electric field.
Reason : In a hollow spherical shield, the electric field inside it is zero at every point.
- [AIIMS 2001]
Assertion : In a cavity within a conductor, the electric field is zero.
Reason : Charges in a conductor reside only at its surface
Assertion : In a cavity within a conductor, the electric field is zero.
Reason : Charges in a conductor reside only at its surface
- [AIIMS 2007]