Charges on Conductors

Q. There are two metallic spheres of same radii but one is solid and the other is hollow, then

1. Solid sphere can be given more charge
2. Hollow sphere can be given more charge
3. They can be charged equally (maximum)
4. None of the above

Q.

Charge always resides on the ………….surface of the conductor.

Q.

Concentric metallic hollow spheres of radii $R$ and $4R$ hold charges $Q_1$ and $Q_2$ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $V\left(R\right)-V\left(4R\right)$ is:

1. $\frac{3Q_2}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$

2. $\frac{3Q_1}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$

3. $\frac{3Q_1}{16{\mathrm{\pi \epsilon }}_0\mathrm{R}}$

4. $\frac{Q_1}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$

Q. A charge of Q coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself

1. Uniformly in the metal object
2. Uniformly on the surface of the object
3. Such that the potential energy of the system is minimised
4. Such that the total heat loss is minimised

Q. A 3 microfarad capacitor is charged to a potential of 300v and 2microfarad capacitor is charged to 200v. The capacitor are then connected in parallel with plates of opposite polarity joined together. What amount of charge will flow; when the plates are so connected?

Q. A hemispherical shell is uniformly charged positively. The electric field at a point on the axis of hemisphere away from the centre is directed:

1. Perpendicular to the diameter
2. Parallel to the diameter
3. At an angle tilted towards the diameter
4. At an angle tilted away from the diameter

Q.

Why like charges repel and opposite charges attract descibe in detail with basic concepts

Q.

What is corona discharge?

Q. $A10\mu \text{F}$ capacitor is fully charged to a potential difference of $50\text{V}$. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes $20\text{V}$. The capacitance of the second capacitor is

1. $15\mu \text{F}$
2. $30\mu \text{F}$
3. $20\mu \text{F}$
4. $10\mu \text{F}$

Q. A long cylindrical shell carries positive surface charge '$\sigma$' in the upper half and negative surface charge '$-\sigma$' in the lower half. The electric field lines around the cylinder will look like
(figures are schematic and not drawn to scale)

1. 
2. 
3. 
4. 

Q.

Can we use transformer to step up DC voltage? Explain.

Q. A network of $4$ capacitors is connected to a battery as shown in the figure. The ratio of charges on $C_2$ and $C_4$ is

1. $\frac{7}{4}$
   
2. $\frac{22}{3}$
3. $\frac{4}{7}$
4. $\frac{3}{22}$

Q. A metal disk with a charge $Q_1=-1e$ is placed near a metal sphere that has a charge $Q_2=-4e$. If the disk touched the sphere, what is the possible final charge on each object?

1. $Q_1=-2e,Q_2=-3e$
2. $Q_1=-3e,Q_2=-3e$
3. $Q_1=-1e,Q_2=+7e$
4. $Q_1=-2e,Q_2=-2e$

Q. Why electrostatic force constant 'k' depends on medium?
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Q.

A thin spherical insulating shell of radius $R$ carries a uniformly distributed charge such that the potential at its surface is $V_o$. A hole with a small area α4πR² (α << 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

1. The potential at the center of the shell is reduced by $2\alpha V_o$
2. The magnitude of electric field at a point, located on a line passing through the hole and shell’s center, on a distance $2R$ from the center of the spherical shell will be reduced by $\frac{\alpha V_0}{2R}$
3. The magnitude of electric field at the center of the shell is reduced by $\frac{\alpha V_o}{2R}$
4. The ratio of the potential at the center of the shell to that of the point at $\frac{1}{2}R$ from center towards the hole will be $\frac{1-\alpha }{1-2\alpha }$

Q. A 6V battery is connected to the terminals of a 3m long wire of uniform thickness and ress†an ce of 100 ohm along with another 100 ohm resistor in series . The difference of potentials between two points on the wire separated by a dis†an ce of 50cm will be

Q. The following arrangement consists of five identical metal plates parallel to each other. Area of each plate is $A$ and separation between the successive plates is $d$. The capacitance between $\text{P}$ and $\text{Q}$ is

1. $\frac{5{ϵ}_{0}A}{d}$
2. $\frac{7}{3}\frac{{ϵ}_{0}A}{d}$
3. $\frac{4}{3}\frac{{ϵ}_{0}A}{d}$
4. $\frac{5}{3}\frac{{ϵ}_{0}A}{d}$

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. Uniformly inside the volume

3. Only on surface but non-uniformly

4. Non-uniformly inside the volume

Q. Between the plates of a parallel plate capacitor of capacitance $C$, two parallel plates of the same metal and area are placed. If the thickness of each plate is equal to $\frac{1}{5}$th of the distance between the parallel plates, the new capacitance is

1. $\frac{5}{3}C$
   
2. $\frac{3}{5}C$
   
3. $\frac{3}{10}C$
   
4. $\frac{10}{3}C$
   

Q. 46. In the circuit shown below C1=10uf, C2=C3=20uf, and C4=40uf.If the charge on C1 is 20uf then potential difference between x and y is

Q.

two identical conducting spheres A and B are separated by a distance greater than their diameters the spheres carry equal charges and electrostatic force between them is F a third identical uncharged sphere C is first brought in contact with A, then with B and finally removed as a result, the electrostatic force between A and B becomes

Q. Three charges of $q_1=1\times {10}^{-6}\text{C}$, $q_2=2\times {10}^{-6}\text{C}$ and $q_3=-3\times {10}^{-6}\text{C}$ have been placed as shown. Then, the net electric flux will be maximum for the surface

1. ${\text{S}}_1$
2. ${\text{S}}_2$
3. ${\text{S}}_3$
4. Same for all three

Q.

What is the S.I unit of electric dipole moment?

Q. In the circuit shown in the figure, initially the switch is open. When the switch is closed, the charge passing through the switch is

1. $120\mu \text{C}$; From $\text{A}$ to $\text{B}$
2. $600\mu \text{C}$; From $\text{B}$ to $\text{A}$
3. $120\mu \text{C}$; From $\text{B}$ to $\text{A}$
4. $60\mu \text{C}$; From $\text{A}$ to $\text{B}$

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. The space between the plates of a parallel plate capacitor of capacitance $C$ is filled with three dielectric slabs of identical size as shown in figure. If the dielectric constants of the three slabs are $K_1$ $K_2$ and $K_3$, find the new capacitance.

1. $C$
2. $(K_1+K_2+K_3)\frac{C}{3}$
3. $(K_1+K_2+K_3)C$
   
4. $(K_1{K}_2+K_2{K}_3+K_3{K}_1)C$

Q.

A hollow sphere has a potential difference 15V then find the potential difference at the centre.

Q. determine the potential difference across the plates of the capacitor C1 of the network show

Q. In the given circuit the potential difference between A and B is 18V and charge on 2 micro farad capacitor is 24 micro coloumb.

Q.

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge Q. (a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell? (b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.