Charges on Large and Parallel Conducting Plates

Q. A parallel plate capacitor is connected with a battery. If the plates of capacitor are shifted apart, then which of the following is the correct statements.

1. The intensity of electric field between the plates decreases and charge on plates also decreases
2. The intensity of electric field between the plates remains constant but charge on the plates increases
3. The intensity of electric field between the plates remains constant but charge on the plates decreases
4. The intensity of electric field between the plates increases but charge on the plates decreases

Q. Find the direction $\theta$ of $\overrightarrow{E}$ at point $\text{P}$ due to uniformly charged finite rod will be at an angle

1. ${30}^{\circ }$ from $\text{x-}$axis
2. ${45}^{\circ }$ from $\text{x-}$axis
3. ${60}^{\circ }$ from $\text{x-}$axis
   
4. none of these

Q.

In an electric field an electron is kept freely . if the electron is replaced by a proton what will be the relationship between the forces experienced by them

Q. two identical helium filled balloons a & b fastened to a weight of 5g by threads floats in equilibrium as shown in the figure calculate the charge on each balloons , assuming that they carry equal charges

Q. Three equal point charges with charge $+q$ each are moving along a circle of radius $R$ and a fixed point charge $-2q$ is placed at the centre of the circle. If $+q$ charges are revolving at constant speed around $-2q$ as shown, then the speed of charges are
(Assume that charges $(+q)$ form vertices of equilateral triangle)

1. $\frac{k{q}^2}{\sqrt{3}Rm}$
2. $\sqrt{\frac{k{q}^2}{Rm}(2-\frac{1}{\sqrt{3}})}$
3. $\sqrt{\frac{k{q}^2}{Rm}(\sqrt{2}+1)}$
4. $\frac{k{q}^2}{2Rm}$

Q. In a process, when two bodies are charged by rubbing against each other, one becomes positively charged while the other becomes negatively charged. Then

1. Mass of each body remains unchanged
2. Mass of positively charged body slightly increases
3. Mass of negatively charged body slightly decreases
4. Mass of each body changes slightly but the total mass of system remains the same

Q.

Two protons A and B are placed in between the two plates of a parallel plate capacitor charged to a potential difference V as shown in the figure. The forces on the protons due to capcitor plates are

1. Equal in magnitude and opposite in direction

2. Equal in magnitude and in same direction

3. Unequal in magnitude and opposite in direction

4. Unequal in magnitude and different in direction

Q. A proton is released at rest $10\text{cm}$ from a charged sheet (perpendicular to it) having uniform electric field around it of intensity $123\text{N/C}$ towards (perpendicular to) the sheet. It will strike the sheet after the time (approximately)
(Charge on proton is $1.6\times {10}^{-19}\text{C}$ and mass of proton is $1.6\times {10}^{-27}\text{kg}$)

1. $4\mu \text{s}$
2. $2\mu \text{s}$
3. $2\sqrt{2}\mu \text{s}$
4. $4\sqrt{2}\mu \text{s}$

Q. The material filled between the plates of a parallel plate capacitor has resistivity $200\Omega \text{m}$. The value of capacitance of the capacitor is $2pF$. If a potential difference of $40\text{V}$ is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is :
$[$Given the value of relative permitivity of material $(k=50)$$]$

1. $9.0\mu \text{A}$
2. $0.9\mu \text{A}$
3. $0.9\text{mA}$
4. $9.0\text{mA}$

Q. Assertion$\left(A\right)$: Four point charges $q_1,q_2,q_3$ and $q_4$ are as shown in figure. The flux over the shown gaussian surface depends only on charges $q_1$ and $q_2$

Reason$\left(R\right)$: Electric field at all points on gaussian surface is depends only on charges $q_1$ and $q_2$


Select the most appropriate answer from the options given below

1. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
2. Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
3. $A$ is true but $R$ is false
4. $A$ is false and $R$ is also false

Q. Find the electric field at the centre of semicircular ring shown in the figure.

1. $\frac{4kq}{\pi R^2}\left(\hat{i}\right)$
2. $\frac{4kq}{\pi R^2}(-\hat{i})$
3. $\frac{2kq}{\pi R^2}(-\hat{i})$
4. $\frac{4kq}{\pi R}(-\hat{i})$

Q. For the given uniformly charged ring, magnitude of the net electric field at point $\text{P}$ is (in $\text{N/C}$)

Q. Find the maximum electric field due to a uniformly charged ring of charge $Q$ and radius $R$ along the axis of the ring $[K=\frac{1}{4\pi {ϵ}_0}]$

1. $\frac{KQ}{3\sqrt{3}{R}^2}$
2. $\frac{2KQ}{\sqrt{3}{R}^2}$
3. $\frac{2KQ}{3\sqrt{3}{R}^2}$
4. $\frac{2KQ}{\sqrt{3}{R}^2}$

Q.

Force acting upon a charged particle kept between the plates of a charged condenser is F. If one plate of the condenser is removed, then the force acting on the same particle will become:

1. 0

2. F/2

3. F

4. 2F

Q.

If the potential difference between the plates of a capacitor is increased by 20%, the energy stored in the capacitor increases by exactly

1. 40%
   

2. 22%
   

3. 44%

4. 20%
   

Q.
Three identical plates are given charges as shown in figure. Charge flown through switch from middle plate when it is closed is.

1. $3Q$
2. $-2Q$
3. $2Q$
4. $0$

Q. The graph between magnitude of electric field intensity due to a positive point charge, as a function of inverse of distance from it is

$[$0.77 Mark$]$

1. Ellipse
2. Hyperbola
3. Parabola
4. Straight Line

Q. An infinite wire having linear charge density $+\lambda$ is arranged as shown. A charge particle of mass $m$ and charge $q$ is released from point $\text{P}$. Find the initial acceleration of the particle $($at $t=0)$ just after the particle is released.
(Assume the straight parts of wire perpendicular to XY plane.)

1. $\frac{q\lambda }{2\pi {ϵ}_{0}mR}\hat{j}$
2. $\frac{q\lambda }{\pi {ϵ}_{0}mR}(-\hat{j})$
3. $\frac{2q\lambda }{\pi {ϵ}_{0}mR}\left(\hat{k}\right)$
4. $\frac{q\lambda }{2\pi {ϵ}_{0}mR}(-\hat{j})$

Q. Consider the system shown below. If the charge is slightly displaced along the perpendicular to the wire from its equilibrium position then find out the time period of $\text{SHM}$ $(k=\frac{1}{4\pi {\epsilon }_o})$.

1. $2\pi \sqrt{\frac{m{d}^2}{k\lambda q}}$
2. $2\pi \sqrt{\frac{m{d}^2}{3k\lambda q}}$
   
3. $\pi \sqrt{\frac{m{d}^2}{2k\lambda q}}$
   
4. $2\pi \sqrt{\frac{m{d}^2}{2k\lambda q}}$
   

Q. A parallel plate capacitor of capacitance $C$ is charged to a potential $V$. The flux of the electric field through a closed surface enclosing the space between capacitor plates is

1. $\frac{CV}{{\epsilon }_0}$
2. $\frac{2CV}{{\epsilon }_0}$
3. Zero
4. $\frac{CV}{2{\epsilon }_0}$

Q. A parallel plate capacitor made of circular plates each of radius $R=6\text{cm}$ has a capacitance $C=100\text{pF}.$ The capacitor is connected to a $230\text{V}AC$ supply with an angular frequency of $300\text{rad/s}$. Determine the amplitude of the magnetic field at point $3\text{cm}$ from the axis between the plates.

1. $3.26\times {10}^{-11}\text{T}$
2. $1.63\times {10}^{-11}\text{T}$
3. $4.89\times {10}^{-11}\text{T}$
4. $8.15\times {10}^{-11}\text{T}$

Q. Given graph shows electric field intensity due to a point charge $\left(E\right)$ at a distance $\left(x\right)$ from it.
Here graphs$(A,B,C,D)$ corresponding to four charges are shown. Which graph represents the charge of higher magnitude?

1. $\text{A}$
2. $\text{B}$
3. $\text{C}$
4. $\text{D}$

Q. If the half portion $\text{ACB}$ of the uniformly charged ring $\text{ADBCA}$ is cut-out then the net electric field due to remaining half portion will be

1. $90\text{N/C}$ along $\text{OC}$
2. $90\text{N/C}$ along $\text{OD}$
3. $180\text{N/C}$ along $\text{OC}$
4. $180\text{N/C}$ along $\text{OD}$

Q. Two conducting plates $\text{A}$ and $\text{B}$ are placed parallel to each other. $\text{A}$ and $\text{B}$ are given charges $10\text{nC}$ and $12\text{nC}$ respectively . Find the distribution of charge on the inner surface of plate $\text{A}$.

1. $-1\text{nC}$
2. $-2\text{nC}$
3. $-3\text{nC}$
4. $-4\text{nC}$

Q.

According to the principle of conservation of charge, the net change in an isolated system ____________

Q. Two points are at distances $a$ and $b$ $(a<b)$ from a long string having linear charge density $\lambda$. The potential difference between the points is proportional to

1. $\frac{b}{a}$
2. $\frac{b^2}{a^2}$
3. $\sqrt{\frac{b}{a}}$
4. $\ln \left(\frac{b}{a}\right)$

Q. 84. Force exerted by a charged particle q1 on another charged particle q2 depend upon the medium between them?

Q. Two protons A and V move parallel to the X-axis in opposite directions with equal speed V. At the instant shown , the magnetic force and electric force acting on the proton A is?? (C=speed of light in vacuum)

Q. Two large conducting sheet are placed parallel to each other with a separation of $2\text{cm}$ between them. An electron starting from rest near one of the sheets reaches the other plate in $2\mu \text{s}$. The surface charge density on the inner surface is
[Assume both sheets have same charge density]

1. $3.1\times {10}^{-13}{\text{C/m}}^2$
2. $4.1\times {10}^{-13}{\text{C/m}}^2$
3. $5.1\times {10}^{-13}{\text{C/m}}^2$
4. $6.1\times {10}^{-13}{\text{C/m}}^2$

Q. A conduting rod $PQ$ of length $l$ intially at rest is dragged with a constant force $F$ along two long smooth parallel rails separated by a distance $l$ as shown in the figure. Then choose the correct statement(s).

1. Terminal velocity of the rod, $V_T=\frac{2FR}{B^2{l}^2}$
2. Terminal velocity of the rod, $V_T=\frac{FR}{B^2{l}^2}$
3. Maximum charge on the capacitor, $q_{max}=\frac{FCR}{Bl}$
4. Maximum charge on the capacitor, $q_{max}=\frac{2FCR}{Bl}$