A solid conducting sphere of radius a has a n | vedclass

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

Question

(A) $1$. Due to electrostatic induction, the inner surface of the spherical shell (at radius $b$) will develop an induced charge equal and opposite to

Vedclass · Accepted Answer

$-\frac{2Q}{4\pi b^2}, \frac{Q}{4\pi c^2}$

Vedclass · Answer

(A) $1$. Due to electrostatic induction, the inner surface of the spherical shell (at radius $b$) will develop an induced charge equal and opposite to the charge on the inner sphere. Since the inner sphere has a charge of $+2Q$, the charge on the inner surface of the shell is $q_{inner} = -2Q$.$2$. The surface charge density on the inner surface is $\sigma_{inner} = \frac{q_{inner}}{4\pi b^2} = -\frac{2Q}{4\pi b^2}$.$3$. The shell has a net charge of $-Q$. Let the charge on the outer surface (at radius $c$) be $q_{outer}$. Since the total charge on the shell is the sum of the charges on its inner and outer surfaces, we have: $q_{inner} + q_{outer} = -Q$, which gives $-2Q + q_{outer} = -Q$, so $q_{outer} = +Q$.$4$. The surface charge density on the outer surface is $\sigma_{outer} = \frac{q_{outer}}{4\pi c^2} = \frac{Q}{4\pi c^2}$.$5$. Thus, the surface charge densities are $-\frac{2Q}{4\pi b^2}$ and $\frac{Q}{4\pi c^2}$. This matches option $A$.

$A$ solid conducting sphere of radius $a$ has a net positive charge $2Q$. $A$ conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere and has a net charge $-Q$. The surface charge density on the inner and outer surfaces of the spherical shell will be

Similar Questions

Two metallic spheres of radii $a$ and $b$ are placed far away from each other and are connected by a thin conducting wire. The total charge on them is $Q$. Calculate the potential of each sphere.

$A$ conducting sphere of radius $10\, cm$ is charged with $10\,\mu C$. Another uncharged sphere of radius $20\, cm$ is allowed to touch it for some time. After the spheres are separated,the ratio of the surface charge densities on the spheres will be:

Consider a metal sphere of radius $R$ that is cut into two parts along a plane whose minimum distance from the sphere's centre is $h$. The sphere is uniformly charged with a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together is:

$A$ charge $+q$ is placed somewhere inside the cavity of a thick conducting spherical shell of inner radius $R_1$ and outer radius $R_2$. $A$ charge $+Q$ is placed at a distance $r > R_2$ from the centre of the shell. Then the electric field in the hollow cavity

$A$ point charge $q$ is placed in a cavity in a metal block. If a charge $Q$ is brought outside the metal,then the electric force experienced by $q$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module