Corona Discharge

Q. Two metal spheres one of radius $R$ and $2R$ respectively. have the same surface charge density $\sigma .$ They are brought in contact and separated. What will be the new surface charge densities on them?

1. ${\sigma }_1=\frac{5}{3}\sigma$ , ${\sigma }_2=\frac{5}{6}\sigma$
2. ${\sigma }_1=\frac{5}{6}\sigma$ , ${\sigma }_2=\frac{5}{2}\sigma$
3. ${\sigma }_1=\frac{5}{2}\sigma$ , ${\sigma }_2=\frac{5}{3}\sigma$
4. ${\sigma }_1=\frac{5}{2}\sigma$ , ${\sigma }_2=\frac{5}{6}\sigma$

Q.

A uniformly charged conducting sphere of $2.4\mathrm{m}$ diameter has a surface density of $80.0\mathrm{\mu C}/{\mathrm{m}}^2$. (a) Find the charge on the sphere (b) What is the total electric flux leaving the surface of the sphere?

Q. Charge between parallel plates :

Surface charge density is defined as the charge per unit surface area of surface charge distribution. i.e., $\sigma =\frac{q}{S}$

Two large thin metal plates are parallel and close to each other, on their inner faces, the plates have surface charge densities of opposite sign having magnitude of $1.70\times {10}^{-22}{\text{Cm}}^{-2}$ as shown in figure.
[Use ${\epsilon }_0=8.85\times {10}^{-12}{\text{Fm}}^{-1}$]

$\left(ii\right)$The electric field $E$ in the region to the left of plate $\text{A}$ and to the right of plate $\text{B}$ is

1. $1.2\times {10}^{-10}{\text{NC}}^{-1};1.2\times {10}^{-10}{\text{NC}}^{-1}$
2. $1.2\times {10}^{-12}{\text{NC}}^{-1};1.2\times {10}^{-12}{\text{NC}}^{-1}$
3. $0.2\times {10}^{-10}{\text{NC}}^{-1};0.2\times {10}^{-10}{\text{NC}}^{-1}$
4. $0{\text{NC}}^{-1};0{\text{NC}}^{-1}$

Q. A metallic sphere of radius $R$ is cut in two parts along a plane whose minimum distance from the sphere's centre is $h=\frac{R}{2}$ and the sphere is uniformly charged with a total electric charge $Q$. The minimum force that should be applied on each of the two parts, to hold the two parts of the sphere together is $\frac{3K{Q}^2}{p{R}^2}$. Then, find the value of $p$

Q. In the figure shown, a spherical conductor has a spherical cavity. A charge $Q$ is placed as shown in figure. Then, choose the correct statement(s):

1. Charge distribution on ${\text{S}}_1$ is uniform and on ${\text{S}}_2$ is non-uniform.
2. Charge distribution on ${\text{S}}_2$ is uniform and on ${\text{S}}_1$ is non-uniform.
3. Charge distributions on both ${\text{S}}_1$ and ${\text{S}}_2$ are uniform.
4. Charge distributions on ${\text{S}}_1$ and ${\text{S}}_2$ are non-uniform.

Q. A non-conducting sphere of radius $R=5\text{cm}$ has its centre at the origin $O$ as shown and have two spherical cavities of radius $r=1\text{cm}$ whose centres are at $(0,3\text{cm})$ and $(0,-3\text{cm})$. If solid material of the sphere has uniform positive charge density $\rho =\frac{1}{\pi }\mu {\text{C-m}}^{-3}$, then potential at point $\text{P}(4\text{cm},0)$ is

1. $35\text{V}$
2. $70\text{V}$
3. $-35\text{V}$
4. $-70\text{V}$

Q. A hollow, insulating spherical shell has a surface charge distribution placed upon it, such that the upper hemisphere has a uniform surface charge density $+\sigma ,$ while the lower hemisphere has a uniform surface charge density $–\sigma ,$ as shown in figure. Their interface lies in x - y plane. Which of the following statement(s) is/are correct?
​​​​​​​

1. Field at all points on z-axis outside the sphere is in positive z-direction
2. The field at all points on x - y plane within the sphere is in negative z direction.
3. Field at points on z-axis which are on either side of origin outside the sphere is in opposite direction
4. For all the points on the x - y plane within the sphere the electric field is not always perpendicular to x-y plane

Q.

Two charged spherical conductors of radii R₁ and R₂ are connected by a wire. The ratio of surface charge densities of the sphere $\frac{{\mathrm{\sigma }}_1}{{\mathrm{\sigma }}_2}$ will be

1. $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$

2. $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$

3. $\sqrt{\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}}$

4. $\frac{{{\mathrm{R}}_1}^2}{{{\mathrm{R}}_2}^2}$

Q. Statement 1: Charge density on a solid conductor is always uniform no matter what the shape.
Statement 2: Charges are always on the surface of a conductor and they repel each other so they always arrange to give uniform charge density.

1. Statement 1 is true. Statement 2 is false
2. Both statements are false
3. Statement 1 is false. Statement 2 is true
4. Both statements are true

Q. Corona discharge is caused by

1. All of the above
2. High charge density causing high electric fields near a metal’s surface.
3. Charges moving into the ionized air under the effect of this electric field.
4. Ionization of gas molecules due to dielectric breakdown

Q. A metallic sphere of radius $R$ is cut in two parts along a plane whose minimum distance from the sphere's centre is $h=\frac{R}{2}$ and the sphere is uniformly charged with a total electric charge $Q$. The minimum force that should be applied on each of the two parts, to hold the two parts of the sphere together is $\frac{3K{Q}^2}{p{R}^2}$. Then, find the value of $p$

Q. Charge between parallel plates :

Surface charge density is defined as the charge per unit surface area of surface charge distribution. i.e., $\sigma =\frac{q}{S}$

Two large thin metal plates are parallel and close to each other, on their inner faces, the plates have surface charge densities of opposite sign having magnitude of $1.70\times {10}^{-22}{\text{Cm}}^{-2}$ as shown in figure.
[Use ${\epsilon }_0=8.85\times {10}^{-12}{\text{Fm}}^{-1}$]

$\left(i\right)$ The electric field $E$ in the region in between the plates $\text{A}$ and $\text{B}$ is

1. $12\times {10}^{-12}{\text{NC}}^{-1}$
2. $2\times {10}^{-10}{\text{NC}}^{-1}$
3. $0.2\times {10}^{-10}{\text{NC}}^{-1}$
4. $1.2\times {10}^{-12}{\text{NC}}^{-1}$

Q. Match the following:

Column-$\text{I}$	Column-$\text{II}$
$\left(\text{i}\right).$ Positively charged Spherical conductor.	$\left(\text{a}\right).$ At the surface , electric field is continuous and maximum.
$\left(\text{ii}\right).$ Spherical non conductor having uniform volume charge distribution.	$\left(\text{b}\right).$ at the surface, electric field is dis-continuous.
$\left(\text{iii}\right).$ Positively charged ring.	$\left(\text{c}\right).$ Electric field is uniform.
$\left(\text{iv}\right).$ Infinite thin sheet of positive charge	$\left(\text{d}\right).$ at the center, electric field is zero.

1. $\text{i}\to \text{a, b},\text{ii}\to \text{d},\text{iii}\to \text{a},\text{iv}\to \text{c}$
2. $\text{i}\to \text{a, c},\text{ii}\to \text{a, d},\text{iii}\to \text{d},\text{iv}\to \text{c}$
3. $\text{i}\to \text{b, d},\text{ii}\to \text{a},\text{iii}\to \text{c},\text{iv}\to \text{d}$
4. $\text{i}\to \text{b, d},\text{ii}\to \text{a, d},\text{iii}\to \text{d},\text{iv}\to \text{c}$

Q. In the given figure, ${\sigma }_1$ and ${\sigma }_2$ are the surface charge densities around points $1$ and $2$ respectively. Then:

1. ${\sigma }_1>{\sigma }_2$
2. ${\sigma }_1<{\sigma }_2$
3. ${\sigma }_1={\sigma }_2$
4. can't be interpreted

Q. Two metallic spheres of same radii, one hollow and one solid, are charged to the same potential. Which will hold more charge?

1. Hollow sphere
2. Both will hold same charge
3. Solid sphere
4. Cannot predict

Q. Two metallic spheres of same radii, one solid and the other hollow are charged to the same potential. Which of the two will hold more charge? Give reasons.

Q. Assertion :When two charged metal spheres are connected by a long wire, then, the surface charge density on each sphere is inversely proportional to the radius. Reason: When two charged metal spheres are connected, charge will flow from one to the other until their potentials are equal.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Corona discharge is caused by

1. Ionization of gas molecules due to dielectric breakdown
2. High charge density causing high electric fields near a metal’s surface.
3. Charges moving into the ionized air under the effect of this electric field.
4. All of the above

Q. Two non-conducting solid spheres of radii $R$ and $2R$, having uniform volume charge densities ${\rho }_1$ and ${\rho }_2$ respectively touch each other. The net electric field at a distance $2R$ from smaller sphere is zero. The ratio $\frac{{\rho }_1}{{\rho }_2},$ is

1. $-\frac{32}{25}$ and -4
2. $-\frac{32}{25}$ and 4
3. $\frac{32}{25}$ and 4
4. $\frac{32}{25}$ and -4

Q. In the figure shown, a spherical conductor has a spherical cavity. A charge $Q$ is placed as shown in figure. Then, choose the correct statement(s):

1. Charge distribution on ${\text{S}}_1$ is uniform and on ${\text{S}}_2$ is non-uniform.
2. Charge distribution on ${\text{S}}_2$ is uniform and on ${\text{S}}_1$ is non-uniform.
3. Charge distributions on both ${\text{S}}_1$ and ${\text{S}}_2$ are uniform.
4. Charge distributions on ${\text{S}}_1$ and ${\text{S}}_2$ are non-uniform.

Q. Which of the following works on the principle of static electricity?
$\left(i\right)$ Lighting conductors
$\left(ii\right)$ Photo copier
$\left(iii\right)$ Electron agent
$\left(iv\right)$ Microphone

1. $\left(i\right)$ and $\left(iv\right)$
2. $\left(i\right)$ and $\left(ii\right)$
3. $\left(ii\right)$ and $\left(iii\right)$
4. $\left(iii\right)$ and $\left(iv\right)$

Q. Statement 1: Charge density on a solid conductor is always uniform no matter what the shape.
Statement 2: Charges are always on the surface of a conductor and they repel each other so they always arrange to give uniform charge density.

1. Both statements are false
2. Statement 1 is true. Statement 2 is false
3. Statement 1 is false. Statement 2 is true
4. Both statements are true

Q. Two copper spheres of the same radii, one hollow and the other solid, are charged to the same potential, then

1. hollow sphere holds more charge
2. both hold equal charge
3. solid sphere holds more charge
4. we cant say

Q. Statement 1: Charge density on a solid conductor is always uniform no matter what the shape.
Statement 2: Charges are always on the surface of a conductor and they repel each other so they always arrange to give uniform charge density.

1. Statement 1 is true. Statement 2 is false
2. Statement 1 is false. Statement 2 is true
3. Both statements are true
4. Both statements are false