Electrostatics

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will

A condenser of capacity C is charged to a potential difference of V₁. The plates of the condenser are then connected to an ideal inductor of inductance L. The current through the inductor when the potential difference across the condenser to V₂ is

An electric dipole is placed at an angle 30°with an electric field intensity 2 x 10⁵ N/C. It experiences a torque equal to 4N-m. The charge on the dipole, if the dipole length is 2cm is,

A spherical conductor of radius 2 m is charged to a potential of 120 V. It is now placed inside another hollow spherical conductor of radius 6 m. Calculate the potential to which the bigger sphere would be raised.

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 centred at the origin of the field will be given by

Calculate the charge on equivalent capacitance of the combination shown in figure between the points P and N.

An isolated sphere has a capacitance of 50 pF. What would be the radius of the sphere?

A parallel plate capacitor has 91 plates, all are identical and arranged with same spacing between them. If the capacitance between adjacent plates is 3 pF. What will be the resultant capacitance?

The distance of the closest approach of an alpha particle fired at a nucleus with kinetic energy K is r₀. The distance of the closest approach when the α particle is fired at the same nucleus with kinetic energy 2K will be

A total charge of 5µC is distributed uniformly on the surface of the thin walled semispherical cup. If the electric field strength at the centre of the hemisphere is 9 × 10⁸ NC⁻¹, then the radius of the cup is
{1/4πε₀ = 9 × 10⁹ N-m²C⁻²}

Potential at a point x-distance from the centre inside the conducting sphere of radius r and carrying a charge Q is

Two small spherical shells A and B are given positive charges of 9C and 4C respectively and placed such that their centres are separated by 10 m. If P is a point in between them, where the electric field intensity is zero, then the distance of the point P from the centre of A is,

A point charge q is situated at a distance r on axis from one end of a thin conductiong rod of length L having a charge Q [uniformly distributed along its length]. The magnitude of electric force between the two is

The S.I. unit of electric flux is

When 10¹⁹ electrons are removed from a neutral metal plate through some process, then the charge on it becomes

Electric field intensity at a point in between two parallel sheets due to like charges of same surface charge densities (σ) is

The acceleration of an electron in an electric field of magnitude 50 V/cm, if e/m value of the electron is 1.76 × 10¹¹ C/kg will be

The angle between the dipole moment and electric field at any point on the equatorial plane is

Pick out the statement which is incorrect?

A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential and capacitance respectively are,

Two conducting spheres of radii 5 cm and 10 cm are given a charge of 15 μC each. After the two spheres are joined by a conducting wire, the charge on the smaller sphere is

A spherical shell of radius 10 cm is carrying a charge q. If the electric potential at distance 5cm, 10cm and 15cm from the centre of the spherical shell is V₁,V₂ and V₃ respectively, then

An electron of mass Mₑ, initially at rest, moves through a certain distance in a uniform electric field in time t₁. A proton of mass Mp also initially at rest, takes time t₂ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t₂/t₁ is nearly equal to

If the electric field lines is flowing along axis of a cylinder, the the flux of this field through the cylindrical surface with the axis parallel to the field is [where r=radius of cylinder]

An inclined plane of length 5.60 m making an angle of 45⁰ with the horizontal is placed in a uniform electric field E=100 Vm⁻¹. A particle of mass 1 kg and charge 10⁻²C is allowed to slide down from the rest position from maximum height of slope. If the coefficient of friction is 0.1, then the time taken by the particle to reach the bottom is

Three capacitors of capacitances 3 μF, 10 μF and 15 μF are connected in series to a voltage source of 100V. The charge on 15 μF is

Two charged spheres seperated at a distance d exert a force F on each other. If they are immersed in a liquid of dielectric constant K=2, then the force (if all conditions are same) is

If a charge on the body is 1 nC, then how many electrons are present on the body?

Two concentric spheres kept in air have radii R and r. They have similar charge and equal surface charge density σ. The electrical potential at their common centre is (where,ε₀=permittivity of free space)

Electric field at a point of distance r from a uniformly charged wire of infinite length having linear charge density λ is directly proportional to

Two charges of equal magnitude q are placed in air at a distance 2a apart and third charge -2q is placed at mid-point. The potential energy of the system is (where, ε₀ = permitivity of free space)

Consider two concentric spherical metal shells of radii r₁ and r₂( r₂>r₁). If the outer shell has a charge q and the inner one is grounded, then the charge on the inner shell is

Two electrons are separated by a distance of 1Å. What is the coulomb force between them?

Two equal and opposite charges of masses m₁ and m₂ are accelerated in a uniform electric field through the same distance. What is the ratio of their accelerations, if their ratio of masses is m₁/m₂=0.5?

An electric dipole of dipole moment p is placed in a uniform external electric field E. Then the,

what is the electric potential at a distance of 9cm from 3nC?

An electric dipole placed in a non-uniform electric field experiences

The electric potential at a point in free space due to a charge Q coulomb is Q x 10¹¹ volts. The electric field at that point is

Three capacitors 3μF, 6μF and 6μF are connected in series to a source of 120 V. The potential difference in volt, across the 3μF capacitor will be

What is the nature of Gaussian surface involved in Gauss’s law of electrostatics?

The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates is E, is

The capacitance of two concentric spherical shells of radii R₁ and R₂ (R₂>R₁) is

The mean free path of electrons in a metal is 4 x 10⁻⁸ m. The electric field which can give on an average 2 eV energy to an electron in the metal will be in units of V/m

An Electric charge does not have which of the following properties?

Two capacitors of 10 pF and 20 pF are connected to 200 V and 100 V sources, respectively. If they are connected by the wire, then what is the common potential of the capacitors?

Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltage of the combination will be

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 of an electron)

The net electric force on a charge of +3μC at the mid-point on the line joining two charges of magnitude +2μC and -2μC separated by the same distance of 6 mm, is

Two point charge +9e and +e are at 16 cm away from each other. Where should another charge q be placed between them so that the system remains in equilibrium?

The electric potential at a point (x,y,z) is given by V = – x²y – xz³ + 4. The electric field E⃗ at that point is

The force of repulsion between two electrons at a certain distance is F. The force between two protons separated by the same distance is (mp=1836 mₑ)

The electric field at a distance 3R / 2 from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance R/2 from the centre of the sphere is

A point charge q is placed at a distance x/2 directly above the centre of a cube of side x. The flux through the cube is

A series combination of n₁ capacitors, each of value C₁, is charged by a source of potential difference 4 V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C₂, in terms of C₁, is then

An electron having charge e and mass m is moving in a uniform electric field E. Its acceleration will be

Electrical force is acting between two charges kept in vacuum. A copper plate is placed between the charges, the force now is

Two identical capacitors are first connected in series and then in parallel. The ratio of equivalent capacitance is

The electric potential V at any point (x,y,z) all in meters in space is given by V = 4x² volt. The electric field at the point (1,0,2) in V/m is

Two parallel metal plates having charges +Q and -Q face 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

Equal charge q each are placed at the vertices AQ and B of an equilateral triangle ABC of side a. The magnitude of electric intensity at the point C is

Two capacitors having capacitances C₁ and C₂ are charged with 120 V and 200 V batteries respectively. When they are connected in parallel now, it is found that the potential on each one of them is zero. Then,

A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is A(m²) the energy (joules) stored in the condenser is

A small oil drop of mass 10⁻⁶kg is hanging in at rest between two plates separated by 1mm having a potential difference of 500 V. The charge on the drop is (g=10ms⁻²)

If two charges +4e and +e are at a distance x apart, then at what distance charge q must be placed from +e, so that it is in equilibrium?

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 θ with the direction of the field. Assuming that the potential energy of the dipole to be zero when = 90⁰, the torque and the potential energy of the dipole will respectively be:

If a mass of 20g having charge 3.0 mC moving with velocity 20 ms⁻¹ enters a region of electric field of 80 NC⁻¹ in the same direction as the velocity of mass then the velocity of mass after 3s in the region will be

Two metal spheres of radii 0.01m and 0.02m are given a charge of 15mC and 45mC, respectively. They are then connected by a wire. The final charge on the first sphere is……x10⁻³C.

The potential energy of particle in a force field is U = A/r² – b/r, where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is:

A rod lies along the X-axis with one end at the origin and the other at x→∞. It carries a uniform charge λCm⁻¹. The electric field at the point x=-a on the axis will be

The concentric spheres of radii R and r have positive charges q₁ and q₂ with equal surface charge densities. What is the electric potential at their common centre?

Two metallic spheres of radii 1 cm and 3 cm are given charges of -1 x 10⁻² C and 5 x 10⁻² C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

A parallel plate capacitor as a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is:

A soap bubble is charged to a potential 12V. If its radius is doubled, then the potential of the bubble becomes

A sphere of 4cm radius is suspended with in a hollow sphere of 6cm radius. If the inner sphere is charged to a potential 3esu while the outer sphere is earthed, then the charge on the inner sphere will be

An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90⁰ is

Charge Q is divided into two parts which are then kept some distance apart. The force between them will be maximum, if the two parts are having the charge

When two identical capacitors are in series, they have 3 μF capacitance and when in parallel 12 μF. What is the capacitance of each?

Work done by an external agent in separating the parallel plate capacitor is

A spherical drop of capacitance 1μF is broken into eight drops of equal radius. Then, the capacitance of each small drop is

A point charge is kept at the centre of a metallic insulated spherical shell. Then

The electric field in a certain region is given by E=5i ̂-3ĵ kV/m. The potential difference Vв-Vᴀ between points A and B, having coordinates (4,0,3)m and (10,3,0)m respectively, is equal to

In a parallel plate capacitor with plate area A and charge Q, the force on one plate because of the charge on the other is equal to

Two capacitors 3μF and 4μF, are individually charged across a 6 V battery. After being disconnected from the battery, they are connected together with the negative plate of one attached to the positive plate of the other.What is the final total energy stored

The electric potential at the surface of an atomic nucleus (z=50) of radius 9.0 x 10⁻¹³ cm is

The unit of electric permittivity is

Two capacitors of capacitances 2 μF and 3 μF are joined in series. Outer plate of first capacitor is at 1000 volt and outer plate of second capacitor is earthed (grounded). Now the potential on inner plate of each capacitor will be

A spherical drop of mercury having a potential of 2.5 v is obtained as a result of merging 125 droplets. The potential of the constituent droplets would be

The unit of permittivity of free space, ε₀ is

The specific charge of a proton is 9.6 x 10⁷ C/kg. The specific charge of an alpha particle will be

A parallel plate capacitor of a capacitance 1 pF has separation between the plates is d. When the distance of separation becomes 2d and wax of dielectric constant x is inserted in it the capacitance becomes 2 pF. What is the value of x?

Two point charges +2 coulomb and +10 coulomb repel each other with a force of 12 N. Charges of -2 coulomb are given to each of these charges, then the force of interaction is

The order of the electric field near the earth’s surface is

The voltage of clouds is 4 x 10⁶ volt with respect to ground. In a lightening strike lasting 100 m sec, a charge of 4 coulombs is delivered to the ground. The power of the lightening strike is

A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates

An electric dipole of moment p is lying along a uniform electric field E. The work done in rotating the dipole by 90° is

Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is

Two identical capacitors each of capacitance 5 mF are charged potentials 2 kV and 1 kV respectively. The -ve ends are connected together. When +ve ends are also connected together, the loss of energy of the system is

Two identical charges repel each other with a force equal to 10 mgwt they are 0.6 m apart in air. (g=10 ms⁻²). The value of each charge is

The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then the potential of each single drop was

Three capacitors each of capacity 4 μF are to be connected in such a way that the effective capacitance is 6 μF. This can be done by

A parallel plate air capacitor is connected to battery. After charging fully, the battery is disconnected and the plates are pulled further apart. The strength of the electric field inside the capacitor would

If the distance between the plates of two capacitor is increased then capacitance

An electric charge 10⁻³ μC is placed at the origin (0,0) of X-Y co-ordinate system. Two points A and B are situated at (√2,√2) and (2,0) respectively. The potential difference between the points A and B will be

A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charges to a potential V volt. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k₁=3 and thickness d/3 while the other one has dielectric constant k₂=6 and thickness 2d/3. Capacitance of the capacitor is now

The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates E, is

The charges Q, +q, and +q are placed at the vertices of an equilateral triangle of side l. If the net electrostatic potential energy of the system is zero, the Q is equal to

Small drops of the same size are charges to V volt each. If n such drops coalesce to form a single large drop, its potential will be

An electric dipole of length 1 cm is placed with the axis making an angle of 30⁰ to an electric field of strength 10⁴ NC⁻¹. If it experiences a torque of Nm, the potential energy of the dipole is

If the force exerted by an electric dipole on a charge q at a distance of 1 m is F, the force at a point 2 m away in the same direction will be