Charge vs Potential in Spherical Conductor

Q. Two metallic spheres of radii $1\text{cm}$ and $3\text{cm}$ are given charges of $-1\times {10}^{-2}\text{C}$ and $5\times {10}^{-2}\text{C}$ respectively. If these are connected by a conducting wire (potential on them becomes equal), the final charge on bigger sphere is

1. $2\times {10}^{-2}\text{C}$
2. $3\times {10}^{-2}\text{C}$
3. $4\times {10}^{-2}\text{C}$
4. $1\times {10}^{-2}\text{C}$

Q. Two charged metal spheres A and B have radii in the ratio 2:3 with charges $5\times {10}^{-6}C$ and $10\times {10}^{-6}C$ respectively. If they are connected by a wire. Then

1. $5\mu C$ of charge flows from B to A till their charges are equal

2. $1\mu C$ of charge flows from A to B till common potential is reached

3. $1\mu C$ of charge flows from B to A till common potential is reached

4. No charge flows between A and B

Q. The radii of two charged metal spheres are 5 cm and 10 cm both having same charge 75 mC. If they are connected by a wire, the quantity of charge transferred through the wire is

1. 25 mC
2. 50 mC
3. 75 mC
4. Zero

Q. The capacitor plates are fixed on an inclined plane and connected to a battery of e.m.f. $E$. The capacitor plates have area $A$, length $l$ and the distance between them is $d$. A dielectric slab of mass $m$ and dielectric constant $k$ is inserted into the capacitor and tied to a mass $M$ by a massless string as shown in the figure. Find the value of $M$ for which the slab will stay in equilibrium. There is no friction between slab and plates.

1. $\frac{m}{2}+\frac{E^2{\epsilon }_{0}A(k-1)}{2lgd}$
2. $\frac{m}{2}-\frac{E^2{\epsilon }_{0}A(k-1)}{2lgd}$
3. $\frac{m}{2}+\frac{E^2{\epsilon }_{0}A(k-1)}{2lgd}$
4. $\frac{m}{2}-\frac{E^2{\epsilon }_{0}A(k-1)}{lgd}$

Q. A system comprises of a solid non conducting sphere of charge $Q$ and radius $R$. A point charge $q$ is placed at a distance $r$ from the centre of sphere. Find the total energy of the system
$[k=\frac{1}{4\pi {\epsilon }_0}]$

1. $\frac{3k{Q}^2}{5R}+\frac{kQq}{R}$
2. $\frac{kQq}{r}$
3. $\frac{3k{Q}^2}{5R}+\frac{kQq}{r}$
4. $\frac{3k{Q}^2}{5R}$

Q.

The insulated metal spheres of radii R₁ and R₂ having charges Q₁ and Q₂ respectively are connected to each other. There is

1. No change in the energy of the system

2. An increase in the energy of the system

3. Always a decrease in the energy of the system

4. A decrease in the energy of the system unless Q₁R₂=Q₂R₁

Q. Two metallic spheres of radii $1\text{cm}$ and $3\text{cm}$ are given charges of $-1\times {10}^{-2}\text{C}$ and $5\times {10}^{-2}\text{C}$ respectively. If these are connected by a conducting wire (potential on them becomes equal), the final charge on bigger sphere is

1. $2\times {10}^{-2}\text{C}$
2. $3\times {10}^{-2}\text{C}$
3. $4\times {10}^{-2}\text{C}$
4. $1\times {10}^{-2}\text{C}$

Q. Two charged metal spheres A and B have radii in the ratio 2:3 with charges $5\times {10}^{-6}C$ and $10\times {10}^{-6}C$ respectively. If they are connected by a wire. Then

1. $5\mu C$ of charge flows from B to A till their charges are equal

2. $1\mu C$ of charge flows from A to B till common potential is reached

3. $1\mu C$ of charge flows from B to A till common potential is reached

4. No charge flows between A and B

Q. Which of the following will have maximum capacitance?

1. A conducting sphere of radius 3 m
2. A conducting sphere of radius 3 mm