Charges on Conductors

Q. A neutral conducting sphere of radius $R$ contains two spherical cavities of radii $a$ and $b$ that contains point charges $q_a$ and $q_b$ placed at the center of each cavity as shown in the figure below . Find the electric field at a distance $r$ outside the conductor.

1. $\frac{q_b}{4\pi {\epsilon }_0{r}^2}$
2. Zero
3. $\frac{q_a+q_b}{4\pi {\epsilon }_0{r}^2}$
4. $\frac{q_a}{4\pi {\epsilon }_0{r}^2}$

Q.

Capacitance depends on which parameters?

Q. An isolated parallel plate capacitor of capacitance $C$ has four surfaces with charges $Q_1,Q_2,Q_3$ and $Q_4$ as shown in the figure below. The potential difference across plates is (In the given diagram, $Q_1$ and $Q_4$ are the charges on the outer surfaces of the left & right plates respectively)

1. $\left|\frac{Q_2}{C}\right|$
2. $\left|\frac{Q_3}{C}\right|$
3. $\frac{[Q_1+Q_2]}{C}$
4. $\left|\frac{Q_2+Q_3}{C}\right|$

Q. An isolated solid metallic sphere is given +Q charge. The charge will be distributed on the sphere

1. Uniformly but only on surface

2. Only on surface but non-uniformly

3. Uniformly inside the volume
4. Non-uniformly inside the volume

Q. A parallel plate capacitor of plate area $5{\text{cm}}^2$ and plate separation $20\text{mm}$ is charged to a potential difference of $10\text{V}$ and then the battery is disconnected. A slab of dielectric constant $5$ is then inserted between the plates to fill the space between the plates completely. What is the work done on the system in the process ?

1. $8.85\times {10}^{-12}\text{J}$
2. $-8.85\times {10}^{-12}\text{J}$
3. $-8.85\times {10}^{12}\text{J}$
4. $8.85\times {10}^{12}\text{J}$

Q. { hi ratio of thermal conductivities of two rods of different material is }5:4. The two rods have same }} rea of cross-section and same thermal resistance. They will have the lengths in the ratio

Q. A parallel plate capacitor of plate area $5{\text{cm}}^2$ and plate separation $20\text{mm}$ is charged to a potential difference of $10\text{V}$ and then the battery is disconnected. A slab of dielectric constant $5$ is then inserted between the plates to fill the space between the plates completely. What is the work done on the system in the process ?

1. $-8.85\times {10}^{12}\text{J}$
2. $8.85\times {10}^{12}\text{J}$
3. $8.85\times {10}^{-12}\text{J}$
4. $-8.85\times {10}^{-12}\text{J}$

Q. A neutral conducting sphere of radius $R$ contains two spherical cavities of radii $a$ and $b$ that contains point charges $q_a$ and $q_b$ placed at the center of each cavity as shown in the figure below . Match the following table:

$\left(\text{i}\right){\sigma }_a$	$\left(\text{a}\right)\frac{q_a+q_b}{4\pi R^2}$
$\left(\text{ii}\right){\sigma }_b$	$\left(\text{b}\right)\frac{-q_a}{4\pi a^2}$
$\left(\text{iii}\right){\sigma }_R$	$\left(\text{c}\right)\frac{-q_b}{4\pi b^2}$

1. $\left(\text{i}\right)-c;\left(\text{ii}\right)-b;\left(\text{iii}\right)-a$
2. $\left(\text{i}\right)-a;\left(\text{ii}\right)-c;\left(\text{iii}\right)-b$
3. $\left(\text{i}\right)-b;\left(\text{ii}\right)-c;\left(\text{iii}\right)-a$
4. $\left(\text{i}\right)-b;\left(\text{ii}\right)-a;\left(\text{iii}\right)-c$

Q. A spherical metal shell of radius $R_A$ and a solid metal sphere of radius $R_B$ $(<R_A)$ are kept far apart and each is given a charge $+\text{Q}$. Then they are connected by a thin wire. Choose the correct option.

1. The electric field inside the shell is zero.
2. Charge on metal shell is greater than charge on solid metal.
3. $\frac{\text{Surface charge density of shell}}{\text{Surface charge density of solid sphere}}=\frac{R_B}{R_A}$
4. All of the above

Q. Four metal conductors having different shapes
1. A sphere
2. Cylindrical
3. Pear
4. Lightning conductor

Which shape will sustain its charge for the longest time?

1. 1
2. 2
3. 3
4. 4

Q.

If a hollow metal sphere is given a charge Q and another conducting sphere is placed inside it concentrically. A charge q is placed at the centre. The charge that appears on the surface B of the inner sphere is

1. -q

2. +q

3. zero

4. +Q

Q. $\text{A}$ and $\text{B}$ are two conductors carrying a current $i$ in the same direction. $x$ and $y$ are two electron beams moving in the same direction. There will be

Q. A point charge $q_1$ is placed inside cavity $1$ and another point charge $q_2$ is inside cavity $2$. If a point charge $q$ is placed outside the conductor then the charge on outer surface of the conductor would be

1. $Q+q_1+q_2$ and it is non-uniformly distributed.
2. $Q+q_1+q_2$ and would be distributed uniformly.
3. $Q+q_1+q_2$ and its uniform or non-uniform distribution depending upon locations of $q_1$ and $q_2$.
4. $Q+q_1+q_2$ and the distribution depends upon the locations of $q_1,q_2$ and $q$.