An isolated solid metal sphere of radius R is given an electric charge. Which of the graphs below best shows the way in which the electric field E varies with distance x from the centre of the sphere?

The electric field intensity at P and Q in the shown arrangement are in the ratio of:

Consider an atom with atomic number Z as consisting of a positive point charge at the centre and surrounded by a distribution of negative charges uniformly distributed within a sphere of radius R. The electric field at a point inside the atom at a distance r from the centre is:

An electron is rotating around an infinite positive linear charge in a circle of radius 0.1 m. If the linear charge density is 1 $\mathrm{\mu C}/\mathrm{m}$, then the velocity of the electron in m/s will be:

When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is:

Two small spheres each carrying a charge q are placed at distance r apart. If one of the spheres is taken around the other in a circular path, the work done will be equal to:

Work done in moving a charge q coulomb on the surface of a given charged conductor of potential V is:

The variation of electric field between the two charges q₁ and q₂ along the line joining the charges is plotted against distance from q₁ (taking rightwards direction of field as positive) as shown, then the correct statement is:

Two identical infinite positive line charges are placed along the lines $x=\pm a$, in the x-y plane. A positive point charge placed at origin is restricted to move along y-axis. Its equilibrium is:

In the figure below, a point charge +Q₁ is at the centre of an imaginary spherical Gaussian surface and another point charge +Q₂ is outside of the Gaussian surface. Point P is on the surface of the sphere. Which one of the following statements is true ?

In a Millikan-type experiment, there are two oil droplets P and Q between the charged horizontal plates, as shown in the diagram. Droplet P is in rest while droplet Q is moving upwards. The polarity of the charges on P and Q is

                     P                Q

In the electric field of a point charge q, a certain charge is carried from point A to B, C, D, and E, the work done:

A positively charged insulator is brougnt near(but does not touch) two metallic spheres that are in contact. The metallic spheres are then separated. The sphere which was initially farthest from the insulator will have:

A proton is kept at rest. A positively charged particle is released from rest at a distance S in its field. Consider two experiments; one in which the charged particle is also a proton and in another, a positron. In the same time t, the work done on the two moving charged particles is

If there were only one type of charge in the universe, then,
a. ${\oint }_{s}E.dS\ne 0$ on any surface.
b. ${\oint }_{s}E.dS=0$ if the charge is outside the surface.
c. ${\oint }_{s}E.dS$ could not be defined.
d. ${\oint }_{s}E.\mathrm{dS}=\frac{q}{{\epsilon }_0}$ if charges of magnitude q were inside the surface.

If 10⁹ electrons move out of a body to another body every second, how much time approximately is required to get a total charge of 1 C on the other body?

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region,
a. the electric field is necessarily zero.
b. the electric field is due to the dipole moment of the charge distribution only.
c. the dominant electric field is $\propto \frac{1}{r^3},$ for large r, where r is the distance from the origin in this region.
d. the work done to move a charged particle along a closed path, away from the region, will be zero.

Refer to the arrangement of charges in the figure and a Gaussian surface of radius R with Q at the centre. Then
        
a. total flux through the surface of the sphere is $\frac{-\mathrm{Q}}{{\epsilon }_0}$.
b. field on the surface of the sphere is $\frac{-Q}{4\pi {\epsilon }_0{R}^2}$.
c. flux through the surface of the sphere due to 5Q is zero.
d. field on the surface of the sphere due to -2Q is the same everywhere.

A positive charge Q is uniformly distributed along a circular ring of radius R. A small test charge q is placed at the centre of the ring. Then,

(a) if q > 0  and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre.
(b) if q < 0 and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring.
(c) if q < 0, it will perform SHM for small displacement along the axis.
(d) q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q > 0.

The electric field at a point on the equatorial plane at a distance \(r\) from the centre of a dipole having dipole moment $\overrightarrow{P}$ is given by:

(r>> separation of two charges forming the dipole, ${\epsilon }_0$= permittivity of free space ) 

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are $1.6 \stackrel{o}{A}$ apart is,

$(m_e\simeq 9\times {10}^{-31} kg, e=1.6\times {10}^{-19} C)$

$(Take \frac{1}{4\pi {\epsilon }_0} = 9\times {10}^9 N{m}^2{C}^{-2})$

In the figure, two positive charges q₂ and q₃ fixed along the y-axis, exert a net electric force in the +x-direction on a charge q₁ fixed along the x-axis. If a positive charge Q is added at (x, 0), the force on q₁

A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by:

The electric flux through the surface

Five charges q₁, q₂, q₃, q₄, and q₅ are fixed at their positions as shown in the figure, S is a Gaussian surface. The Gauss' law is given by ${\int }_{\mathbf{S}}\mathbf{E}.\mathrm{d}\mathbf{S}=\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$. Which of the following statements is correct?

The figure shows electric field lines in which an electric dipole p is placed as shown. Which of the following statements is correct?

A point charge +q is placed at a distance d from an isolated conducting plane. The field at a point P on the other side of the plane is:

A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed:

If ${\int }_{\mathbf{S}}\mathbf{E}.\mathrm{d}\mathbf{S}=0$ over a surface, then

(a) the electric field inside the surface and on it is zero

(b) the electric field inside the surface is necessarily uniform

(c) the number of flux lines entering the surface must be equal to the number of flux lines leaving it

(d) all charges must necessarily be outside the surface

The electric field at a point is:

(a) always continuous

(b) continuous if there is no charge at that point

(c) discontinuous only if there is a negative charge at that point

(d) discontinuous if there is a charge at that point