Potential Energy of Two Point Charges

Q. Figure shows a system of three concentric metal shells $A,B$ and $C$ with radii $a,2a$ and $3a$ respectively. Shell $B$ is earthed and shell $C$ is given a charge $Q$. Now if shell $C$ is connected to shell $A$, then the final charge on the shell $B\text{is}\frac{-Qx}{11}$, where the value of $x$ is

Q.

What is the potential energy of an electric dipole in a uniform electric field?

Q. Two identical conducting spheres having unequal positive charges $q_1$ and $q_2$ separated by distance $r$. If they are made to touch each other and then separated again to the same distance. The electrostatic force between the spheres in this case will be (neglect induction of charges)

1. More than before
2. Less than before
3. Zero
4. Same as before

Q.

Define the term electric potential. Give its SI unit.

Q. In a Millikan's oil drop experiment , an oil drop of mass $0.64\times {10}^{-14}\text{kg}$ carrying a charge $1.6\times {10}^{-19}\text{C}$ remains stationary between two plates separated by a distance of $5\text{mm}.$ The voltage that must be applied between the plates is-
[Take $g=9.8{\text{ms}}^{-2}$ ]

1. $1960\text{V}$
2. $980\text{V}$
3. $3920\text{V}$
4. $2880\text{V}$

Q. A radionuclide with disintegration constant $\lambda$ is produced in a reactor at a constant rate $\alpha (=2\lambda )$ nuclei per second. At t = 0, there are no nuclei present in the reactor. During each decay energy $E_0$ is released. 20% of this energy is utilized in increasing the temperature of water. Assume that there is no loss of energy through water surface. (Given $E_0=100$ times the energy required to raise the temperature of mass m of water from
$0^{\circ }C$ to ${100}^{\circ }C$).

Expression of energy released in time t is

1. $E_0[\alpha t-\frac{\alpha }{\lambda }(1-e^{-\lambda t}\left)\right]$
   
2. $2E_0[\alpha t-\frac{\alpha }{\lambda }(1-e^{-\lambda t}\left)\right]$
   
3. $\frac{E_0}{2}[\alpha t-\frac{\alpha }{\lambda }(1-e^{-\lambda t}\left)\right]$
   
4. $\frac{E_0}{4}[\alpha t-\frac{\alpha }{\lambda }(1-e^{-\lambda t}\left)\right]$

Q. As shown in the figure, a dust particle with mass $m=5.0\times {10}^{-9}kg$ and charge $q_0=2.0nC$ starts from the rest at point $‘a^{\prime }$ and moves in a straight line to point $b$. What is its speed $v$ at point $b$?

1. $34m{s}^{-1}$
2. $26m{s}^{-1}$
3. $46m{s}^{-1}$
4. $14m{s}^{-1}$

Q. A small metal sphere, carrying a net charge of $q_1=-2\mu C$, is held in a stationery position by insulating supports. A second small metal sphere, with a net charge of $q_2=-8\mu C$ and mass $1.50g$ is projected towards $q_1$. When the two spheres are $0.800\text{m}$ apart, $q_2$ is moving towards $q_1$ with speed $20m{s}^{-1}$ as shown in the figure. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.
How close does $q_2$ get to $q_1$?

1. $0.20\text{m}$
2. $0.30\text{m}$
3. $0.10\text{m}$
4. $0.15\text{m}$

Q.

Two charged particles, having equal charges of $2.0\times {10}^{-5}C$ each , are brought from nfinity to within a separation of 10 cm. Find the increase in the electric potential energy during the process.

Q. When separation between two charges is increased, the electric potential energy

1. Increases
2. Decreases
3. Remains the same
4. May increase or may decrease

Q.

In a polar molecule, the ionic charge is $4.8\times {10}^{-10}$ e.s.u. If the inter-ionic distance is $1\stackrel{\mathrm{o}}{\mathrm{A}}$ unit, then the dipole moment is

1. 41.8 D

2. 4.18 D

3. 4.8 D

4. 0.48 D

Q.

Four identical charged particles having same mass are located at four corners of a regular tetrahedron. If only one of the particles is released, with the remaining tetrahedron fixed, it acquires a final speed of $V_o.$ If all the charges are released together, their final speed will be $\frac{V_o}{n}$, then n is

Q.

A charge of +10 C is fixed at the origin. Choosing the reference point at A(1, 2), the change in potential energy of the system when a charge of +1C is taken from A to infinity is?

1. Positive
2. Negative
3. Zero
4. None of these

Q. The sun radiates energy at the rate of $3.6\times {10}^{26}{\text{Js}}^{-1}$. The rate of decrease in mass of sun is $\left({\text{in kgs}}^{-1}\right)$

1. $3.6\times {10}^{36}$
2. $12\times {10}^{10}$
3. $1.3\times {10}^{20}$
4. $4\times {10}^9$

Q. A small metal sphere, carrying a net charge of $q_1=-2\mu C$, is held in a stationery position by insulating supports. A second small metal sphere, with a net charge of $q_2=-8\mu C$ and mass 1.50g is projected towards $q_1$. When the two spheres are $0.800\text{m}$ apart, $q_2$ is moving towards $q_1$ with speed $20m{s}^{-1}$ as shown in the figure. Assume that the two spheres can be treated as point charges. You can ignore the force of gravity.
The speed of $q_2$ when the spheres are 0.400 m apart is

1. $2\sqrt{10}m{s}^{-1}$
2. $2\sqrt{6}m{s}^{-1}$
3. $4\sqrt{10}m{s}^{-1}$
4. $4\sqrt{6}m{s}^{-1}$

Q. Assuming potential energy at infinite separation is zero, what is the Potential Energy of a two charge system if the charges are both +10C and are separated by 10m?

1. None of these
2. 
3. 
4. 

Q. Three charges +4q, Q and q are placed in a straight line of length L at points 0, L/2, L distance from one end respectively. What should be Q in order to make the net force on q to be zero?

Q. Two identical small conducting spheres, having charges of opposite sign, attract each other with a force of $0.108N$ when separated by $0.5m$. The spheres are connected by a conducting wire, which is then removed, and thereafter, they repel each other with a force of $0.036N$. The initial charges of the spheres are :

1. $\pm 5\times {10}^{-6}Cand\mp 15\times {10}^{-6}C$
2. $\pm 1.0\times {10}^{-6}Cand\mp 3.0\times {10}^{-6}C$
3. $\pm 0.5\times {10}^{-6}Cand\mp 1.5\times {10}^{-6}C$
4. $\pm 2.0\times {10}^{-6}Cand\mp 6.0\times {10}^{-6}C$

Q. A uniformly charged thin ring of linear charge density $+\lambda$ is shown in figure. An electron is placed on the ring's axis at a distance of $r$ from the centre of the ring and is constrained to stay on the axis of the ring. The motion of the electron when it is released from the rest is

1. Along straight line and continuous to move toward +x axis.
2. Oscillatory about O
3. Along straight line and continuous to more toward - x axis
4. The electron will remain stationary.

Q.

Q.

What is the work done by electric force in taking a charged particle of charge 1C by 10 cm along the equator of a dipole?

Q. If we say that the electric potential of a point in space is 10 V, what do you understand from it? (Take potential at infinity as 0V)

1. The amount of work done by external agent, in bringing a 10 C charge from infinity to that point (slowly) is 10J
2. The amount of work done by external agent, in bringing a unit positive charge from infinity to that point (slowly) is 10 J
3. The net magnitude of force acting on a unit positive charge at that point is 10 N
4. The net work done to being a unit positive chargefrom infinity to that point (slowly) is 10 J

Q.

Which of the following sets of quantities have same dimensional formula ?

1. Frequency, angular frequency and angular momentum

2. Surface tension, stress and spring constant

3. Acceleration, momentum and retardation

4. Thermal capacity, specific heat and entropy

5. Work, energy and torque

Q. Two identical small conducting spheres having unequal positive charges $q_1$ and $q_2$ are separated by a distance r. If they are now made to touch each other and then separated again to the same distance, the electrostatic force between them in this case will be :

1. less than before
2. same as before
3. more than before
4. zero

Q. The magnitude of electric field intensity E, such electron, placed in the field, would experience an electric force equal to its weight is :

1. $5.6\times {10}^{-7}N{C}^{-1}$
2. $5.6\times {10}^{-8}N{C}^{-1}$
3. $5.6\times {10}^{-10}N{C}^{-1}$
4. $5.6\times {10}^{-11}N{C}^{-1}$

Q.

State and define the SI unit of potential.

Q. Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electricpotential zero? Take the potential at infinity to be zero.

Q. Two force point charges $+q$ and $+4q$ are a distance $\ell$ apart. A third charge $q_1$ is so placed that the entire system is in equilibrium. Find the location, magnitude and sign of the third charge.

1. $q_1=\frac{4}{9}q$
2. $q_1=\frac{-4}{9}q$
3. $q_1$ is to be placed at a distance $\ell /3$ from $q$.
4. $q_1$ is to be placed at a distance $\frac{2\ell }{3}$ from $4q$.

Q. The electrostatic force on a metal sphere of charge $0.4$ $\mu$C due to another identical metal sphere of charge $-0.8$ $\mu$C in air is $0.2$N. Find the distance between the two spheres and also the force between the same two spheres when they are brought into contact and then replaced in their initial positions.

Q. Assertion :According to law of conservation of mechanical energy change in potential energy is equal and opposite to the change in the kinetic energy. Reason: Mechanical energy is not conserved quantity.

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