Electric Potential Due to Charged Infinite Sheets

Q. A hollow charged conductor has tiny hole cut into its surface. Show that electric field in hole is (sigma upon 2 epsilon) n where n is the unit vector in the outward normal direction, and sigma is the surface charge density near the hole.

Q. Figure shows two equipotential lines in $\text{XY}$ plane for an electric field. The scales are marked. The $\text{X-}$component $E_x$ and $\text{Y-}$component $E_y$ of the electric field in the space between these equipotential lines are respectively.

1. $+100{\text{Vm}}^{-1}$, $-200{\text{Vm}}^{-1}$
2. $+200{\text{Vm}}^{-1}$, $+100{\text{Vm}}^{-1}$
3. $-100{\text{Vm}}^{-1}$, $+200{\text{Vm}}^{-1}$
4. $-200{\text{Vm}}^{-1}$, $+100{\text{Vm}}^{-1}$

Q. A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B. At the position MNQ, the speed of the ring is V and the potential difference developed across the ring is

1. Zero
2. $BV\pi R^2/2$ and M is at higher potential
   
3. $\pi RBV$ and Q is at higher potential
   
4. 2RBV and Q is at higher potential

Q. ntTwo charges 12uC and 8 uC are 10cm apart. Find the work done to move the charges 4cm closer.n

Q. A solid uniformly charged fixed non conducting sphere of total charge $Q$ and radius $R$ contains a tunnel of negligible diameter. If a point charge $-q$ of mass ${}^{\prime }{m}^{\prime }$ is released at rest from point $P$ as shown in figure then its velocity at the surface of the sphere is found to be $\sqrt{(\frac{nqQ}{12\pi {\epsilon }_{0}Rm})}$. Find the value of $n$ (Give integer value)

Q. Statement (1) : For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on the axis of the ring is zero.
Statement (2) : For a non-uniformly charged thin circular ring with net charges as zero, electric field at any point on the axis of the ring is zero.

1. $\left(1\right)$ is true, $\left(2\right)$ is false.
2. $\left(1\right)$ is false, $\left(2\right)$ is true.
3. Both statements are true.
4. Both statements are false.
   

Q. The electrostatic potential inside a charged spherical ball is given by $V=a{r}^2+b$, where $r$ is the distance from the centre; $a$ and $b$ are constants. Then the charge density inside ball is

1. $-6a{\epsilon }_{0}r$
2. $-24\pi a{\epsilon }_{0}r$
3. $-6a{\epsilon }_0$
4. $-24\pi a{\epsilon }_0$

Q. Two point charges q and -q are held stationary at separation d. The work done by electric force as the spacing changes to 2d is

Q. A point charge $q$ is surrounded by eight identical charges at a distance $r$ as shown in figure. How much work is done by the forces of electrostatic repulsion when the point charge at the center is removed to infinity?

1. $\frac{8q^2}{4\pi {\epsilon }_{0}r}$
2. $\frac{18q^2}{4\pi {\epsilon }_{0}r}$
3. $\frac{64q^2}{4\pi {\epsilon }_{0}r}$
4. Zero

Q. The side of the cube is ${}^{\prime }{l}^{\prime }$ and point charges are kept at each corner as shown in diagram. Interactive electrostatic potential energy of all the charges is $\frac{4k{q}^2}{\sqrt{N}l}$, then $N$ is

Q. A charged sphere of radius $0.02\text{m}$ has charge density of $1{\text{Cm}}^{-2}$. The workdone when a charge of $40\text{nC}$ is moved from infinity to a point that is at a distance of $0.04\text{m}$ from the centre of the sphere.

1. $1.44\pi \text{J}$
2. $2\text{J}$
3. $14.4\pi \text{J}$
4. $1.44\text{J}$

Q. Quarter non-conducting disc of radius 4R having uniform surface charge density $\sigma$ is placed in xz-plane, then which of the following is correct?

1. Electric potential at $(0,3R,0)is\frac{\sigma R}{4{ϵ}_0}$
2. Electric potential at $(0,0,0)\text{is}\frac{\sigma R}{2{ϵ}_0}$
3. Electric field at (0, 3R, 0) is symmetric with x and z axis
4. Electric field intensity at (-4R, 0, -4R) is equally inclined with x and z axis

Q. A sphere is uniformly charged with charge per unit volume as $\rho$ and radius $R$. The electrostatic potential energy stored inside the sphere is $\frac{4\pi {\rho }^2{R}^5}{n{ϵ}_0}$. Fill the value of $n$

Q. An elelctric field $\overrightarrow{E}=50\hat{i}+75\hat{j}{\text{NC}}^{-1}$ exist in a certain region of space. Assume that the potential at the origin to be zero. The potential at a point $\text{P}$$(1\text{m},2\text{m})$will be

1. $100\text{V}$
2. $-100\text{V}$
3. $200\text{V}$
4. $-200\text{V}$

Q. A particle of mass m and charge q moves at a high speed along the X axis. Initially it is near -infinity and then in a short time moves to positive infinity. Another charge Q is fixed at (0, -d) . As the moving charge passes the stationary charge, the X component of its velocity does not change appreciably but it acquires a small velocity in the y direction. Determine the angle through which the moving charge is deflected.

Q.

A small particle of charge q is displaced from the centre of a uniformly charged solid sphere of radius R and charge Q to an outside point at a distance R from the surface of sphere... Find the word done.

Q.

The potential difference between two oppositely charged infinite sheets, with charge density σ and separation D, is proportional to?

​

1. 1/σ

2. σ

3. 1/D

4. \N

Q. One coulomb charge is placed on an insulated stand at the centre of the spherical conductor of radius 1 m this year is given a charge of 1 c the electrostatic force experienced by the charge at the centre will be

Q. Two identical charges are placed 3m apar in air experiences a Coulombs force of 9*10 N. The magnitude of charge is

Q. 87.The surface area of a body is 25 CM square and its surface density of charge is 5 CGS unit what is the total charge on it?

Q. Assuming reference point (for calculating electric potential) to be at infinity, mark the correct statement(s)

1. Electric potential at the centre of a uniformly charged spherical shell due to its own charge is zero.
2. Electric potential at the centre of a uniformly charged sphere due to its own charge is zero.
3. Self energy of a dipole is positive.
4. If we change the reference point, the potential difference between 2 points will not change.

Q. Assuming reference point (for calculating electric potential) to be at infinity, mark the correct statement(s)

1. If we change the reference point, the potential difference between 2 points will not change.
2. Electric potential at the centre of a uniformly charged spherical shell due to its own charge is zero.
3. Electric potential at the centre of a uniformly charged sphere due to its own charge is zero.
4. Self energy of a dipole is positive.

Q. Two parallel sheets $1$ and $2$ carry uniform charge densities ${\sigma }_1$ and ${\sigma }_2$$({\sigma }_1>{\sigma }_2)$ as shown in figure. The electric field in the region marked $II$ is

1. $-\frac{({\sigma }_1+{\sigma }_2)}{2{\epsilon }_0}$
2. $-\frac{\left({\sigma }_1{\sigma }_2\right)}{2{\epsilon }_0}$
3. $\frac{({\sigma }_1+{\sigma }_2)}{2{\epsilon }_0}$
4. $\frac{({\sigma }_1-{\sigma }_2)}{2{\epsilon }_0}$

Q. Three concentric metallic spherical shells $\text{A, B}$ and $\text{C}$ of radii $a,b$ and $c(a<b<c)$ have surface charge densities $-\sigma ,+\sigma$, and $-\sigma$ respectively. The potential of shell $\text{A}$ is:

1. $\frac{\sigma }{{ϵ}_0}(a+b-c)$
2. $\frac{\sigma }{{ϵ}_0}(a-b+c)$
3. $\frac{\sigma }{{ϵ}_0}(b-a-c)$
4. None

Q. Two equal point charges A and B are R distance apart.a third point charge placed on the perpendicular distance at a distance d from the centre will experience maximum electrostatic force when?

Q. Quarter non-conducting disc of radius 4R having uniform surface charge density $\sigma$ is placed in xz-plane, then which of the following is correct?

1. Electric potential at $(0,3R,0)is\frac{\sigma R}{4{ϵ}_0}$
2. Electric potential at $(0,0,0)\text{is}\frac{\sigma R}{2{ϵ}_0}$
3. Electric field at (0, 3R, 0) is symmetric with x and z axis
4. Electric field intensity at (-4R, 0, -4R) is equally inclined with x and z axis

Q. The electric potential due to a uniform disc of surface charge density $0.5C/m^2$ and radius 3 cm, at a point 4 cm from the centre on its perpendicular axis is

1. 
2. 
3. 
4. 

Q. Calculate the electric potential at point A where x = - d.

Q. Two concentric thin conducting spherical shells having radius $R$ and $2R$ are shown in figure. A charge $+Q$ is given to shell $A$ and $-4Q$ is given to shell $B$. Now shell $A$ and $B$ are connected by a thin conducting wire, then the final charge on the sphere $B$ will be :

1. $\frac{-3Q}{2}$
2. $-4Q$
3. $-3Q$
4. $2Q$

Q. A hollow charged conductor has a tiny hole cut into its surface .Show that the electric field in the hole is ( σ/Eo)n where n is the unit vector in the outward normal direction and σ is the surface charge density near the hole.