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Two-point charges +8q and –2q are located at x = 0 and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is 
1. 8 L
2. 4 L
3. 2 L
4. $\frac{L}{4}$

An electric dipole is put in north-south direction in a sphere filled with water. Which statement is correct ?
(1) Electric flux is coming towards sphere
(2) Electric flux is coming out of sphere
(3) Electric flux entering into sphere and leaving the sphere are same
(4) Water does not permit electric flux to enter into sphere

Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in 
(1)   (2)
(3)    (4)

Four charges are arranged at the corners of a square ABCD, as shown in the adjoining figure. The force on the charge kept at the centre O is:
      

Charge q is uniformly distributed over a thin half-ring of radius R. The electric field at the centre of the ring is 
(1) $\frac{q}{2{\pi }^2{\epsilon }_0{R}^2}$
(2) $\frac{q}{4{\pi }^2{\epsilon }_0{R}^2}$ 
(3) $\frac{q}{4\pi {\epsilon }_0{R}^2}$
(4) $\frac{q}{2\pi {\epsilon }_0{R}^2}$

A positively charged ball hangs from a silk thread. We put a positive test charge q₀ at a point and measure F/q₀, then it can be predicted that the electric field strength E 
(1) > F/q₀
(2) = F/q₀
(3) < F/q₀
(4) Cannot be estimated

Two infinitely long parallel wires having linear charge densities λ₁ and λ₂ respectively are placed at a distance of R meters. The force per unit length on either wire will be $\left(K=\frac{{\displaystyle 1}}{{\displaystyle 4\pi {\epsilon }_0}}\right)$
(1) $K\frac{2{\lambda }_1{\lambda }_2}{R^2}$
(2) $K\frac{2{\lambda }_1{\lambda }_2}{R}$
(3) $K\frac{{\lambda }_1{\lambda }_2}{R^2}$ 
(4) $K\frac{{\lambda }_1{\lambda }_2}{R}$

Out of gravitational, electromagnetic, Vander Waals, electrostatic and nuclear forces; which two are able to provide an attractive force between two neutrons 
(1) Electrostatic and gravitational
(2) Electrostatic and nuclear
(3) Gravitational and nuclear
(4) Some other forces like Vander Waals

A total charge \(Q\) is broken in two parts \(Q_1\) and \(Q_2\) and they are placed at a distance \(R\) from each other. The maximum force of repulsion between them will occur, when:

Three charges \(4q,Q,\) and \(q\) are in a straight line in the position of \(0,l/2,\) and \(l\) respectively. The resultant force on \(q\) will be zero if \(Q\) equal to:
1. \(-q\)
2. \(-2q\)
3. \(\frac{-q}{2}\)
4. \(4q\)

Two charges each of 1 coulomb are at a distance 1 km apart, the force between them is 
(1) 9 × 10³ Newton
(2) 9 × 10^–3 Newton
(3) 1.1 × 10^–4 Newton
(4) 10⁴ Newton

Two charges \(+2\) C and \(+6\) C are repelling each other with a force of \(12\) N. If each charge is given \(-2\) C of charge, then the value of the force will be:

The force between two charges 0.06 m apart is 5 N. If each charge is moved towards the other by 0.01 m, then the force between them will become:

Two equally charged, identical metal spheres A and B repel each other with a force 'F'. The spheres are kept fixed with a distance 'r' between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is 
(1) F
(2) 3F/4
(3) F/2
(4) F/4

The magnitude of electric field intensity E is such that, an electron placed in it would experience an electrical force equal to its weight is given by 
(1) mge
(2) $\frac{mg}{e}$
(3) $\frac{e}{mg}$
(4) $\frac{e^2}{m^2}g$

An uncharged sphere of metal is placed in between two charged plates as shown. The lines of force look like 

(1) A
(2) B
(3) C
(4) D

The figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero?


(1) 1
(2) 2
(3) 3
(4) 4

An electric charge q is placed at the centre of a cube of side a. The electric flux on one of its faces will be:
(1) $\frac{q}{6{\epsilon }_0}$
(2) $\frac{q}{{\epsilon }_0{a}^2}$
(3) $\frac{q}{4\pi {\epsilon }_0{a}^2}$
(4) $\frac{q}{{\epsilon }_0}$ 

Total electric flux coming out of a unit positive charge put in air is 
(1) ${\epsilon }_0$
(2) ${\epsilon }_0^{-1}$
(3) ${\left(4p{\epsilon }_0\right)}^{-1}$
(4) $4\pi {\epsilon }_0$ 

A cube of side l is placed in a uniform field E, where $E=E\hat{i}$. The net electric flux through the cube is
(1) Zero
(2) l²E
(3) 4l²E
(4) 6l²E

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is 

(1) $3q/{\epsilon }_0$
(2) $2q/{\epsilon }_0$
(3) $q/{\epsilon }_0$ 
(4) Zero

Consider the charge configuration and spherical Gaussian surface as shown in the figure. While calculating the flux of the electric field over the spherical surface, the electric field will be due to: 

(1) q₂ only
(2) Only the positive charges
(3) All the charges
(4) +q₁ and – q₁ only

Two-point charges +q and –q are held fixed at (–d, 0) and (d, 0) respectively of a (x, y) coordinate system. Then 
(1) E at all points on the y-axis is along $\hat{i}$
(2) The electric field $\overrightarrow{E}$ at all points on the x-axis has the same direction
(3) Dipole moment is 2qd directed along $\hat{i}$
(4) Work has to be done in bringing a test charge from infinity to the origin

The electric field due to a uniformly charged solid sphere of radius R as a function of the distance from its centre is represented graphically by -
(1)  (2)
(3)  (4)

Six charges are placed at the corner of a regular hexagon as shown. If an electron is placed at its centre O, force on it will be:

1. Zero
2. Along OF
3. Along OC
4. None of these

Suppose the charge of a proton and an electron differ slightly. One of them is \(\text- e\) and the other is \((e+\Delta e)\). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance \(d\) (much greater than atomic size) apart is zero, then $$\(\Delta e\) is of the order: [Given the mass of hydrogen, ${}_{}$\(m_h = 1.67\times 10^{-27}~\text{kg}\)]
1. \(10^{-20}~\text{C}\)
2. \(10^{-23}~\text{C}\)
3. \(10^{-37}~\text{C}\)
4. \(10^{-47}~\text{C}\)

An electric dipole is place at an angle of \(30^{\circ}\) with an electric field intensity \(2\times10^{5}~\text{N/C}\). It experiences a torque equal to \(4~\text{Nm}\). The charge on the dipole, if the dipole length is \(2~\text{cm}\), is: 

Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d(d < < l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then, v varies as a function of the distance x between the sphere, as:
(a) \(v \propto x\)
(b) \(v \propto x^{\frac{-1}{2}}\)
(c) \(v \propto x^{-1}\)
(d) \(v \propto x^{\frac{1}{2}}\)${\frac{\mathrm{}}{}}^{}$
 

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become:

1. (1/√2)²
2. $(r/\sqrt[3]{2})$
3. (2r/√3)
4. (2r/3)

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta =90°$, the torque and the potential energy of the dipole will respectively be
1. $pE \sin \theta ,-pE \cos \theta$
2. $pE \sin \theta ,-2pE \cos \theta$
3. $pE \sin \theta ,2pE \cos \theta$
4. $pE \cos \theta ,-pE \sin \theta$

The electric field in a certain region is acting radially outward and is given by E=Ar. A charge contained in a sphere of radius 'a' centered at the origin of the field will be given by
1. $4\pi {\in }_{o}A{a}^2$
2. $\pi {\in }_{o}A{a}^2$
3. $4\pi {\in }_{o}A{a}^3$
4. ${\in }_{o}A{a}^2$

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will
1. be reduced to half                                 
2. remain the same
3. be doubled
4. increase four times

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)
1. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2 }{e^2}$                  2. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fe}}^2}{d^2}}$
3. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{e^2}}$               4. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{q^2}$
 

 
A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is 

(1) 3E along KO 
(2) E along OK 
(3) E along KO
(4) 3E along OK  

Two parallel metal plates having charges +Q and -Q faces each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will
(1) become zero                                   
(2) increase
(3) decrease                                         
(4) remain same

A hollow insulated conducting sphere is given a positive charge of $10 \mathrm{\mu C}$. What will be the electric field at the centre of the sphere if its radius is 2 m?
1. zero
2. $5 {\mathrm{\mu Cm}}^{-2}$
3. $20 {\mathrm{\mu Cm}}^{-2}$
4. $8 {\mathrm{\mu Cm}}^{-2}$

When air is replaced by a electric medium of constant K, the maximum force of attraction between two charges, separated by a distance,
1. decreases K times
2. increase K times
3. remains unchanged
4. becomes $\frac{1}{K^2}$ times

The figure shows some of the electric field lines corresponding to an electric field. The figure suggests 

(1) E_A > E_B > E_C
(2) E_A = E_B = E_C
(3) E_A = E_C > E_B
(4) E_A = E_C < E_B

Torque acting on electric dipole moment $\overrightarrow{\mathrm{p}}$ placed in uniform electric field $\overrightarrow{\mathrm{E}}$ is
1. $\overrightarrow{\mathrm{p}}\times \overrightarrow{E}$
2. $\overrightarrow{\mathrm{p}}.E$
3. $\overrightarrow{\mathrm{p}}\times \overrightarrow{E}\times \overrightarrow{\mathrm{p}}$
4. $\frac{\overrightarrow{\mathrm{E}}.\overrightarrow{\mathrm{p}}}{{\mathrm{p}}^2}$

An electric dipole has the magnitude of its charge as q and its dipole moment is $\overrightarrow{\mathrm{p}}$. It is placed i a uniform electric field $\overrightarrow{\mathrm{E}}$. If its dipole moment is along the direction of the field the force on it and its potential energy are, respectively
1. $\mathrm{q}.\overrightarrow{\mathrm{E}} \mathrm{and} \overrightarrow{\mathrm{p}}.\overrightarrow{\mathrm{E}}$
2. zero and minimum
3. $\mathrm{q}.\overrightarrow{\mathrm{E}} \mathrm{and} \mathrm{maximum}$
4. $\mathrm{q}.\overrightarrow{\mathrm{E}} \mathrm{and} \mathrm{minimum}$

A hollow cylinder has a charge q coulomb within it. If $\varnothing$ is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of voltmeter will be

1. $\frac{\mathrm{q}}{2{\mathrm{\epsilon }}_0}$
2. $\frac{\varnothing }{3}$
3. $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}-\varnothing$
4. $\frac{1}{2}\left(\frac{q}{{\epsilon }_0}-\varnothing \right)$

A square surface of side L meter in the plane of the paper is placed in a uniform electric field E $\left({\mathrm{Vm}}^{-1}\right)$ acting along the same plane at an angle $\mathrm{\theta }$ with the horizontal side of the square as shown in figure. The electric flux linked to the surface, in units of Vm, is

1. zero
2. ${\mathrm{EL}}^2$
3. ${\mathrm{EL}}^2\mathrm{cos\theta }$
4. ${\mathrm{EL}}^2\mathrm{sin\theta }$

What is the flux through a cube of side 'a' if a point charge of q is at one of the corners?
1. $\frac{2q}{{\epsilon }_0}$
2. $\frac{q}{8{\epsilon }_0}$
3. $\frac{q}{{\epsilon }_0}$
4. $\frac{q}{2{\epsilon }_0}6a^2$

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow{\mathrm{E}}$. Due to the force $\mathrm{q}\overrightarrow{\mathrm{E}}$, its velocity increases from 0 to 6 m ${\mathrm{s}}^{-1}$ in one second duration. At that instant the direction of the field is reversed. The car continues to move for two seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively.
1. $1 m s^{-1}, 3.5 m s^{-1}$
2. $1 m s^{-1}, 3 m s^{-1}$
3. $2 m s^{-1}, 4 m s^{-1}$
4. $1.5 m s^{-1}, 3 m s^{-1}$