Potential Energy of a Point Charge Placed at a Point with Non Zero Potential

Q. Two point-charges $+9e$ and $+e$ are is kept $16\text{cm}$ apart from each other. Where should a third charge $\text{q}$ be placed between them so that the system is in the equilibrium state?

1. $24\text{cm from}+9e$
2. $12\text{cm from}+9e$
3. $24\text{cm from}+e$
4. $12\text{cm from}+e$

Q.

When an alpha particle of mass M moving with velocity V bombards a heavy nucleus of charge Ze its distance of closest approach from the nucleus depends on M As:

Q. Two point charges $+9q$ and $+q$ are kept $16\text{cm}$ apart. Where should a third charge $q_0$ be placed between them so that the system remains in equilibrium?

1. $6\text{cm}$ from $+9q$
2. $12\text{cm}$ from $+9q$
3. $6\text{cm}$ from $+q$
4. $12\text{cm}$ from $+q$

Q. An alpha particle is accelerated through a potential difference of ${10}^6$ volt. Its kinetic energy will be

1. 1 MeV
2. 8 MeV
3. 4 MeV
4. 2 MeV

Q. An electron (charge = $1.6\times {10}^{-19}$ coulomb) is accelerated through a potential of 1, 00, 000 volts. The energy required by the electron is

1. $1.6\times {10}^{-24}$ joule
2. $1.6\times {10}^{-14}$ joule
3. $0.53\times {10}^{-14}$ joule
4. $1.6\times {10}^{-14}$ joule

Q. If an electron starts from rest from a point at which potential is 50 volt to another point at which potential is 70 volt, then its kinetic energy in the final state will be

1. $3.2\times {10}^{-10}J$
   
2. $3.2\times {10}^{-18}J$
3. $1J$
4. $1dyne$

Q. A uniform electric field of magnitude $250\text{V/m}$ is directed in the positive $\text{x-}$direction. A $+12\mu \text{C}$ charge moves from the origin to the point $(x,y)=(20.0\text{cm},$$5.0\text{cm})$. What is the total work done required in moving the charge particle to the new position?

1. $-0.6\text{mJ}$
2. $0.4\text{mJ}$
3. $4\mu \text{J}$
4. $6\mu \text{J}$

Q. For the shown system of fixed charges, where should a third charge of $3nC$ be placed, so that the system remains in equilibrium.

1. $0.37$ $\text{m}$ from $4nC$ charge toward left
2. $0.47$ $\text{m}$ from $4nC$ charge toward left
3. $0.57$ $\text{m}$ from $4nC$ charge toward left
4. $0.67$ $\text{m}$ from $4nC$ charge toward left

Q.

An electron (mass$=9.1\times {10}^{-31}\mathrm{kg}$) is sent into an electric field of intensity $9.1\times {10}^6\mathrm{N}/\mathrm{C}$. The acceleration produced is

1. $1.6\times {10}^{18}{\mathrm{ms}}^{-2}$

2. $1.6\times {10}^6{\mathrm{ms}}^{-2}$

3. $1.6\times {10}^{-18}{\mathrm{ms}}^{-2}$

4. $1.6\times {10}^{-6}{\mathrm{ms}}^{-2}$

Q.

The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is

1. 2 : 1

2. 3 : 1

3. 8 : 1

4. 4 : 1

Q. A pellet carrying charge of 0.5 coulombs is accelerated through a potential of 2, 000 volts. It attains a kinetic energy equal to

1. 1000 ergs
2. 1000 joules
3. 1000 kWh
4. 500 ergs

Q. Two charges $Q$ coulomb and $-Q$ coulomb are placed on a straight line as shown in the figure. Choose the correct graphical representation of potential $\left(V\right)$ versus distance $\left(r\right)$.

1. 
2. 
3. 
4. 

Q. The mean free path of conduction electrons in copper is about $4\times {10}^{-8}\text{m}$. For a copper block, find the electric field which can give, on an average, $1\text{eV}$ energy to conduction electrons.

1. $2.5\times {10}^7{\text{Vm}}^{-1}$
2. $2.5\times {10}^{-7}{\text{Vm}}^{-1}$
3. $5\times {10}^{-7}{\text{Vm}}^{-1}$
4. $5\times {10}^7{\text{Vm}}^{-1}$

Q. Two identical thin rings, each of radius $R$, are coaxially placed a distance $R$ apart . If $Q_1$ and $Q_2$ are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of the other is equal to

1. Zero
2. $\frac{q(Q_1-Q_2)(\sqrt{2}-1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$
3. $\frac{q(Q_1-Q_2)(\sqrt{2}+1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$
4. $\frac{q(Q_1+Q_2)(\sqrt{2}-1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$

Q. Three identical dipoles with charges $q$ and $-q$ and separation $a$ between the charges are placed at the corners of an equilateral triangle of side $d$ as shown in fig. Find the interaction energy of the system $(a<<d)$.

1. $\frac{3q^2{a}^2}{4\pi {\epsilon }_0{d}^3}$
2. $\frac{3q^2{a}^2}{\pi {\epsilon }_0{d}^3}$
3. $\frac{q^2{a}^2}{7\pi {\epsilon }_0{d}^3}$
4. $\frac{q^2{a}^2}{2\pi {\epsilon }_0{d}^3}$

Q.

Electric potential in electrostatic is analogous to _________ in heat.

Q. Find the potential difference $V_a-V_b$ between points $a$ and $b$ as shown below.

1. $16\text{V}$
2. $8\text{V}$
3. $-8\text{V}$
4. $-16\text{V}$

Q. The plates $\text{A}$ and $\text{B}$ of a parallel plate capacitor (PPC) as shown in the figure contain charges $\text{+Q}$ and $\text{-Q}$ respectively. The plate $\text{A}$ is fixed and the plate $\text{B}$ is connected to one end of a spring of spring constant $K$. The other end of the spring is connected to a rigid support. If the system is released from rest, what is the maximum elongation produced in the spring? The area of each plate is $\text{A}$ and the medium between the plates is air.

1. $\frac{Q^2}{2KA{\epsilon }_o}$
2. $\frac{Q^2}{KA{\epsilon }_o}$
3. $\frac{2Q^2}{KA{\epsilon }_o}$
4. $\frac{Q^2}{4KA{\epsilon }_o}$

Q. A body of mass 4 gm carrying a charge 1$\mu$ C starts from rest at the positive plate and reaches the negative plate of a parallel plate condenser with final velocity of 0.3 m/s. The potential difference between the plates is?

1. 180 V
2. 360 V
3. 90 V
4. 18 V

Q. The mean free path of conduction electrons in copper is about $4\times {10}^{-8}m$. For a copper block, find the electric field which can give, on an average, $1eV$ energy to a conduction electons.

1. $2.5\times {10}^7{\text{Vm}}^{-1}$
2. $2.5\times {10}^{-7}{\text{Vm}}^{-1}$
3. $5\times {10}^{-7}{\text{Vm}}^{-1}$
4. $2.5\times {10}^{-7}{\text{Vm}}^{-1}$

Q. A Carnot engine, having an efficiency of $\eta =1/10$ as heat engine, is used as a refrigerator. If the work done on the system is $10J$, the amount of energy absorbed from the reservoir at lower temperature is

1. $99J$
2. $90J$
3. $100J$
4. $1J$

Q. Two point charges q${}_1$ and q${}_2$ are placed at a distance 'd' apart as shown in the figure. The electric field intensity is zero at a point 'P' on the line joining them as shown. If the ratio $\frac{q_1}{q_2}$ is $-{\left(\frac{xr+d}{r}\right)}^2$. Find the value of $x$.

Q. Given the diagram below with positive and negative charges separated by the distance d, how much work (in Joules) would the electric field created by the pictured charges do on a separate $+1.0C$ charge in moving it from point A to point B?
The blue charge is negative. The red charge is positive.
Answer are expressed in terms of k (the coulomb constant) and given distances

1. $\frac{k}{2d}$
2. $\frac{-k}{2d}$
3. $\frac{k}{4d}$
4. $\frac{-k}{d}$
5. $\frac{-k}{4d}$

Q. A spherical shell with an inner radius 'a' and an outer radius 'b' is made of conducting material. A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell.
(a) Charge $-q$ is distributed on the surfaces as
(A) $-Q$ on the inner surface, $-Q$ on outer surface
(B) $-Q$ on the inner surface, $-q+Q$ on outer surface
(C) $+Q$ on the inner surface, $-q-Q$ on outer surface
(D) The charge $-q$ is spread uniformly between the inner and outer surface.
(b) Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. The electrostatic potential at a distance $R(a<R<b)$ from the centre of the shell is $[whereK=\frac{1}{4\pi {\epsilon }_0}]$

1. $0$
2. $\frac{KQ}{a}$
3. $K\frac{Q-q}{R}$
4. $K\frac{Q-q}{b}$

Q.

Equal and similar charges are placed on the earth and the moon. The numerical value of charge required to neutralise their gravitational attraction is (Given: mass of earth$=6\times {10}^{24}kg$, Mass of moon$=7\times {10}^{22}kg$) :

1. $\frac{1}{5.3}\times {10}^{-13}C$
2. $9.3\times {10}^{13}C$
3. $5.5\times {10}^{13}C$
4. $3.6\times {10}^{13}C$

Q.

Two equal charges q of opposite sign are separated by a small distance '$2l$'. The electric potential at a point on the perpendicular bisector of the line joining the two charges at a distance r is :

1. Zero
2. $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{r}$
3. $\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$
4. $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{r^2}$

Q. Two identical thin rings, each of radius $R$ metres are coaxially placed at distance $R$ metres apart. If $Q_1$ coulumb and $Q_2$ coulumb are respectively, the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of the other

1. zero
2. $\frac{q(Q_1-Q_2)(\sqrt{2}-1)}{4\sqrt{2}\pi {ϵ}_{0}r}$
3. $\frac{q(Q_1-Q_2)(\sqrt{2}+1)}{4\sqrt{2}\pi {ϵ}_{0}r}$
4. $\frac{q\sqrt{2}(Q_1+Q_2)}{4\sqrt{2}\pi {ϵ}_{0}r}$

Q. A charged particle of mass ‘m’ and charge ‘q’ is released from rest in an electric field of uniform strength E.
The kinetic energy of the particle after time ‘t’ is ___

1. $\frac{2E^2{t}^2}{mg}$
2. $\frac{E^{2}m{q}^2}{2t^2}$
3. $\frac{Eqm}{2t}$
4. $\frac{E^2{q}^2{t}^2}{2m}$

Q.

If a 3C charge moves from a point of potential $V_1$ to another point of potential $V_2$, the change in P.E of the system will be?

1. $3V_1$

2. $3(V_2-V_1)$

3. $3V_2$

4. $3(V_1-V_2)$

Q.

Where is the electric potential zero?