Potential Energy of a System of Multiple Point Charges

Q. Two point charges 100μc and 5μc are placed at points A and B respectively with AB=40 cm . The work done by external force in displacing the charge 5μc from B to C , where BC=30 cm, angle $ABC=\frac{\pi }{2}and\frac{1}{4\pi {ϵ}_0}=9\times {10}^{9}N{M}^2/c^2$

1. 
2. 
3. 
4. 

Q.

What is the difference between potential difference and voltage?

Q. 24.Identify the wrong statement A) The electrical potential energy of a system of two protons shall increase if the separation between the two is decreased B) the electrical potential energy of a Proton electron system will increase if the separation between the two is decreased c) the electrical potential energy of a Proton electron system will increase if the separation between the two is increased D) the electrical potential energy of system of two electrons shall increase if the separation between the two is decreased

Q. Three charges Q + q and +q are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

1. $\frac{-2q}{2+\sqrt{2}}$
   
2. $\frac{-q}{1+\sqrt{2}}$
   
3. $-2q$
   
4. $+q$

Q.

A moving charge will gain kinetic energy due
to the application of :-
(1) Electric field
(2) Magnetic field
(3) Both of these
(4) None of these

Q. Proton, deuteron and alpha particle of the same kinetic energy are moving in circular field. The radii of proton, deuteron and alpha particle are respectively $r_p$, $r_d$ and $r_{\alpha }$. Which one of the following relations is correct?

1. $r_{\alpha }=r_p=r_d$
2. $r_{\alpha }=r_p<r_d$
3. $r_{\alpha }>r_d>r_p$
4. $r_{\alpha }=r_d<r_d$

Q. Electric charges of $1\mu C,-1\mu C$ and $2\mu C$ are placed in air at the corners $A,B$ and $C$ of an equilateral triangle having length of each side $10cm$ respectively. The resultant force on the charge at $C$ is

1. $0.9N$
2. $3.6N$
3. $2.7N$
4. $1.8N$

Q. Two small spheres each carrying a charge Q are placed 1 m apart. The electric force between them is F. If one sphere is taken around the other, the work done is. A)F. B)2F. C) F/2. D) Zero

Q. Three charges $($two of same nature$)$ are arranged on a straight line are in equilibrium. This nature of equilibrium is

1. stable
2. unstable
3. neutral
4. Any of the above

Q.

Potential energy is a scalar quantity.

1. True
2. False

Q.

Is potential energy a vector quantity?

Q. In a hydrogen atom, the electron and proton are bound at a distanceof about 0.53 Å: (a) Estimate the potential energy of the system in eV, taking thezero of the potential energy at infinite separation of the electronfrom proton. (b) What is the minimum work required to free the electron, giventhat its kinetic energy in the orbit is half the magnitude ofpotential energy obtained in (a)? (c) What are the answers to (a) and (b) above if the zero of potentialenergy is taken at 1.06 Å separation?

Q.

Two equal charges of magnitude Q each are placed at a distance d apart. Their electrostatic energy is E. A third charge $-\frac{Q}{2}$ is brought midway between these two charges. The electrostatic energy of the system is now

1. -2E

2. -E

3. 0

4. E

Q. A charged partial is moving in a uniform magnetic field in a circular path with a radius R.when energy of the particle is doubled, then the new radius will be A)R2 B)R/2 C)2R D)R/2

Q. Three charges each of charge ‘q’ are placed at the corners of an equilateral triangle. The fourth charge to be placed at the centre of the triangle so that electrostatic potential energy of the system is zero is

1. $\frac{q}{\sqrt{3}}$
2. $\frac{-q}{\sqrt{3}}$
3. $q$
4. $\frac{-q}{\sqrt{2}}$

Q.

What does potential difference in a capacitor really mean? Is it the work done in bringing Q charge from infinity?

Q. An infinite number of charges, each numerically equal to $q$ and of the same sign, are placed along the x-axis at $x=1\text{m},x=2\text{m},x=4\text{m},x=8\text{m}$ and so on. Then the electrical potential at $x=0$ due to this set of charges is ( Assume that $\frac{1}{4\pi {ϵ}_0}=k$)

1. $2kq$
2. $\frac{2kq}{5}$
3. $\frac{4kq}{3}$
4. $\frac{4kq}{5}$

Q. Two charges $q_1$ and $q_2$ are placed 30 cm apart as shown in the figure. A third charge $q_3$is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{q_3}{4\pi {ϵ}_0}k$, where k is

1. $6q_2$
2. $8q_2$
3. $6q_1$
4. $8q_1$

Q.

A charge q is located above the centre of a square plate of side a, at a distance $\frac{a}{2}$. The flux of electric field through the plate Is?

1. q/ε₀

2. q/2ε₀

3. q/4ε₀

4. q/6ε₀

Q.

The protons are brought towards each other. Will the P.E. of the system decrease or increase?

Q.

A neutral hydrogen molecule has two protons and two electrons. If one of the electrons is removed we get a hydrogen molecular ion $\left(H_2^{+}\right)$ . In the ground state of $H_2^{+}$ the two protons are separated by roughly $1.5$$A^o$ and the electrons is roughly $1$ $A^o$ from each proton. The potential energy of the system is :

1. $-9.6eV$
2. $-19.2eV$
3. $zero$
4. $-38.4eV$

Q. Two point charges $q_1$ and $q_2$ are placed at a distance of $50\text{m}$ from each other in air, and interact with a certain force $F$. The same charges are now put in oil whose relative permittivity is $5.0$. Find the new force of interaction between them :

1. $F$
2. $\frac{F}{5}$
3. $5F$
4. $\frac{F}{\sqrt{5}}$

Q. Two charges each of magnitude $Q$ are fixed apart at a distance of '$2a$'. A third charge ($-q$ of mass ${}^{\prime }{m}^{\prime }$) is placed at the midpoint of the two charges. Now if $-q$ charge is slightly displaced perpendicular to the line joining the charges then, find its time period.

Q. Two charges of magnitude 5 nC and -2 nC, one placed at points (2 cm, 0, 0) and (x cm, 0, 0) in a region of space, where there is no other external field. If the electrostatic potential energy of the system is -0.5 $\mu$J. The value of x is:

1. 16 cm
2. 4 cm
3. 20 cm
4. 80 cm

Q. Three charges Q, +q and +q are placed at the vertices of a right angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to (IIT-JEE 2000)

1. $\frac{-q}{1+\sqrt{2}}$
2. $\frac{-2q}{2+\sqrt{2}}$
3. -2q
4. +q

Q. During the transition of an electron from higher state to lower state, a photon is emitted having energy equal to

1. the energy difference between the initial and final states.
2. the energy of the electron in the initial state.
3. the energy of the electron in the final state.
4. the sum of energies in the initial and the final states.

Q. Four equal charges $q$ each are placed at four corners of square of side $a$ each. Work done in carrying a charge $-q$ from its centre to infinity is

1. $zero$
2. $\frac{\sqrt{2}q}{\pi {ϵ}_{0}a}$
3. $\frac{q^2}{2\pi {ϵ}_{0}a}$
4. $\frac{\sqrt{2}{q}^2}{\pi {ϵ}_{0}a}$

Q. Three point charges q, -2q and -2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be

1. $\frac{1}{4\pi {ϵ}_0}.\frac{2q^2}{a}$
2. $Negative$
3. $\frac{1}{4\pi {ϵ}_0}.\frac{3q^2}{a}$
4. $Zero$

Q. Two charges $q_1$ and $q_2$ are placed $30\text{cm}$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\text{cm}$ from $C$ to $D$. The change in the potential energy of the system is $\frac{q_3}{4\pi {ϵ}_0}k$, where $k$ is

1. $8q_2$
2. $6q_2$
3. $8q_1$
4. $6q_1$

Q. Two positive point charges of $12\mu C$ and $8\mu C$ are $10cm$ apart. The work done in bringing them $4cm$ closer is

1. $5.8J$
2. $5.8eV$
3. $13J$
4. $13eV$