Two concentric spherical shells of radius R_1 | vedclass

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

Question

(D) Let the charge on the inner shell after closing the key be $q_1'$.Since the inner shell is connected to the ground, its potential becomes zero.The

Vedclass · Accepted Answer

$-\left( q_1 + q_2 \frac{R_1}{R_2} \right)$

Vedclass · Answer

(D) Let the charge on the inner shell after closing the key be $q_1'$.Since the inner shell is connected to the ground, its potential becomes zero.The potential of the inner shell is given by the sum of potentials due to its own charge and the charge on the outer shell:$V_1 = \frac{k q_1'}{R_1} + \frac{k q_2}{R_2} = 0$From this, we get:$\frac{q_1'}{R_1} = -\frac{q_2}{R_2} \implies q_1' = -q_2 \frac{R_1}{R_2}$The charge that flows through the key is the change in charge on the inner shell:$\Delta q = q_{final} - q_{initial} = q_1' - q_1$$\Delta q = -q_2 \frac{R_1}{R_2} - q_1 = -(q_1 + q_2 \frac{R_1}{R_2})$Thus, the magnitude of charge flowing to the ground is $(q_1 + q_2 \frac{R_1}{R_2})$.

Two concentric spherical shells of radius $R_1$ and $R_2$ have $q_1$ and $q_2$ charge respectively as shown in the figure. How much charge will flow through key $k$ when it is closed?

Similar Questions

$A$ hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in the figure. Let $V_A, V_B$,and $V_C$ be the potentials at points $A, B$,and $C$ respectively,where $A$ and $B$ are on the surface of the sphere and $C$ is inside the sphere. Then:

Two conducting spheres $A$ and $B$ have radii $1 \, mm$ and $2 \, mm$ respectively and are charged. They are placed at a distance of $5 \, cm$. When they are connected by a conducting wire,the ratio of the electric field intensities on their surfaces at equilibrium is:

$A$ metallic sphere $A$ isolated from the ground is charged to $+50 \mu C$. This sphere is brought into contact with another isolated metallic sphere $B$ of half the radius of sphere $A$. Then the charge on the two isolated spheres $A$ and $B$ are in the ratio:

$A$ 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:

Vedclass Test Series

Exam Paper Generator

Online Exam Module