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QUESTION: 1

Two equally charged identical metal spheres A and B repel each other with a force 2 * 10^{-5} N. Another identical uncharged sphere C is touched to B and then placed at the mid point between A and B. The net electric force on C is ______ .

Solution:

As the sphere C is touched to sphere B ; the charge on B & C will be distributed equally.

QUESTION: 2

A point charge q sits at a corner of a cube of side a, as shown in the figure on the right, the flux of the electric field vector through the shaded side is

Solution:

When a charge is situated at the corner of any face, then its contribution at the centre of cubic is 1/4 q

QUESTION: 3

The electric flux crossing the wire frame ABCD of length l width b and whose centre is at a distance OP = d from an infinite line of charge with linear charge density λ consider that the plane of frame is perpendicular to line OP is ______ .

Solution:

QUESTION: 4

The electric potential in a region is represented as v = 2x + 3y -z, obtain expression for the electric field strength?

Solution:

QUESTION: 5

A uniform dielectric ball is placed in a uniform electric field of strength under these conditions the dielectric becomes polarized uniformly. The electric field strength inside the ball is ____.

Solution:

QUESTION: 6

A parallel plate air capacitor is made using two square plates each of side 0.2m, spaced 1 cm apart. It is connected to a 50 V battery. What is the energy stored in the capacitor?

Solution:

QUESTION: 7

A particle of positive charge Q = Ze where, Z is an integer is having a fixed position P. Another charged particle of mass m and charge e moves at a constant speed in a circle of radius r_{1}, with centre at P. Find the work that must be done to increase the radius of circle to r_{2}.

Solution:

Let q orbit round Q in a circle of radius r

K.E. of orbiting particle = 1/2 mv^{2}

Now total energy of q when in orbit of radius r_{1
}

When it is in orbit of radius r_{2}

The workdone on q = charge in energy

QUESTION: 8

A plane electromagnetic wave travelling in a vacuum is characterized by the electric and magnetic fields

It ω and k are positive, then the value of H_{0} must be

Solution:

for electromagnetic wave

Here having same phase and moving perpendicular to each other

QUESTION: 9

Consider two charges +Q and -Q placed at the points (a.O) and (-a.O) in a plane, as shown is the figure on the right. If the origin is moved to the point (x.y). the magnitude of the dipole moment of the given charge distribution with respect to this origin will be

Solution:

When origin is shifted at 0(x,y) point, then potential and Electric field will be changed. But dipole moment is the multiple charge on dipole and their separation, which not change in that condition.

QUESTION: 10

Two concentric coplanar semicircular conductors from part of two current loops as shown in figure. If there radii are 11 cm and 4 cm. The magnetic induction at the centre is (in 10^{-5} w_{b}/m^{2})

Solution:

Magnetic field at the centre of a circular coil =

magnetic field at the centre due to wire

Total magnetic field at the centre =

Putting values

QUESTION: 11

A long straight conductor is bent at angle of 90^{0} as shown in the figure. The magnetic field induction at A is

Solution:

QUESTION: 12

A beam of protons with a velocity 4 x 10^{5} m/sec. Enters a uniform magnetic field of 0.3 T at an angle 60^{0 }to the magnetic field. The pitch of helix is?

Solution:

Pitch of the helix = (V_{II}) (timeperiod)

Putting values we get;

Pitch

QUESTION: 13

An a.c. voltage source is connected across a parallel plate capacitor. The value of displacement current is —

Solution:

let the a.c. voltage source connected across the plates o b a capacitor is

The capacity of a parallel plate capacitor with an area b. section A and plate separation d is

Electric field E in the dielectric medium between plate is

QUESTION: 14

If the earth receives 2 cal min^{-1} cm^{-2 }solar energy. The amplitude of magnetic fields of radiation is

Solution:

Poynting vector as

The energy per unit area per second is

QUESTION: 15

The magnetic field associated with the electric field vector is given by

Solution:

QUESTION: 16

The current flowing in a coil of self-inductance L is given by ampere. where a and A are constants. The potential difference between the ends of the coil will be:

Solution:

QUESTION: 17

Solving Poisson's equation for the electrostatic potential in a region with a constant charge density two students find different answers.

The reason why these different solutions are both correct is because

Solution:

We know that the poission's equation is

If a potential function satisfied the Laplace equation then

If means that the given potential function will exist in a charge less system. If not. then it will satisfies the poission's equation and we can calculate the charge density (ρ)

The given function are

But the boundary conditions are different in both cases. The boundary condition are along to x-axis. But one function satisfies by the Laplace's eq. and one function satisfies by the Poisson's eq. so we cannot add both solutions.

QUESTION: 18

An electric dipole is constructed by fixing two circular charged rings, each of radius a, with an insulating contact (see figure). One of these rings has total charge +Q and the other has total charge -Q. If the charge is distributed uniformly along each ring, the dipole moment about the point of contact will be

Solution:

We will consider this two rings as point charges (because the charge is distributed uniformly on them) placed at the centre of these rings, so, we have dipole moment

QUESTION: 19

The field potential in a certain region of space depends only on the x coordinate as where a and b are constants.

Then charge density ρ(x) is

Solution:

...(i)

from gauss theorem

...(ii)

dq is charge contained between the sphere of radii x and x + dx.

...(iii)

So, from eq. (1)(2) and (3)

QUESTION: 20

Charge is distributed uniformly throughout the long non-conducting cylinder of radius R. Which one of the following graphs best represents the magnitude of the resulting electric field E as a function of r, the distance from the axis of the cylinder?

Solution:

QUESTION: 21

The total potential due to an electric dipole "p" placed at the origin is known to be the form f(r) The total flux of the electric field through a spherical surface of radius 'R' with the dipole at the centre is given by :-

Solution:

Total flux = 0 → ( As Q_{net} inside the surface is zero)

QUESTION: 22

In the following circuit, the AC source is an ideal voltage source. What is the amplitude of the steady state current through the inductor at resonance

Solution:

QUESTION: 23

The capacitance of a cylindrical capacitor whose is comprised of two cylindrical shells of radius r_{1} & r_{2} length (I) is (r_{1} < r_{2})

Solution:

QUESTION: 24

An infinitely long hollow cylinder of radius a carrying a surface change density σ is rotated about its cylindrical axis with a constant angular speed ω. Then the magnitude of vector potential outside the cylinder at a distance r from its axis is

Solution:

Surface current

Magnetic field inside is

QUESTION: 25

The electric and magnetic fields in the space are

being unit vectors in x and y directions respectively. The Poynting vector in this region is

Solution:

The rate of transmission of electromagnetic energy per unit area through a plane perpendicular to the direction of propagation of the electromagnetic waves is known as poynting vector denoted by letter and is given as

E = E X H ...(i)

where ...(ii)

and

⇒ ...(iii)

QUESTION: 26

A plane electromagnetic wave has the magnetic field given by

where k is the wave number and are the Cartesian unit vectors in X, Y and Z-directions, respectively.

Then, the electric field corresponding to the above wave, is given by

Solution:

QUESTION: 27

If points in x- direction and points in Z-direction. and a particle of mass m and charge Q at rest is released from origin, then particle will follow cycloidal path. Which of the following coupled differential equation represents cycloidal path ( where )

Solution:

QUESTION: 28

A thin conducting wire is bent into a circular loop of radius r and placed in a time-dependent magnetic field of magnetic induction Such that the plane of loop is perpendicular to Then the induced emf in the loop is

Solution:

QUESTION: 29

If at t = 0. the charge density in a medium having conductivity σ and permittivity ε is then the charge density at any later time t is given by

Solution:

equation of continuity is

QUESTION: 30

A plane electromagnetic wave has the magnetic field given by

where k is the wave number and are the Cartesian unit vectors in x, y and z directions, respectively, then the corresponding electric field is given by

Solution:

*Multiple options can be correct

QUESTION: 31

Two non-conducting solid sphere of radii R and 2R, having uniform volume charge densities P_{1} and P_{2} respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centre of the sphere, is zero. The ratio P_{1}/P_{2} can be

Solution:

If resultant electric field is zero, then

*Multiple options can be correct

QUESTION: 32

A field line is shown in the figure. This field cannot represent

Solution:

Electrostatic and gravitational field do not make closed loops.

*Multiple options can be correct

QUESTION: 33

Two identical metal plates are given positive charges Q_{1} & Q_{2} ( < Q_{1}) respectively. If they are how brought closer together to from a parallel plate capacitor with capacitance (C) then

Solution:

*Multiple options can be correct

QUESTION: 34

Which of the statements are correct?

An electromagnetic wave incident upon a perfectly absorbing surface exerts

Solution:

When electromagnetic wave are incident on the surface of a substance, they are absorbed or reflected and thus transfer momentum to the substance. The rate at which momentum is transferred per unit area is known as radiation pressure if U is energy density then Radiation pressure prad = u

poynting vector S = cu

Prad α S

and z =|E/H| = 3 76 (constant)

*Multiple options can be correct

QUESTION: 35

A Spherical metal shell A of radius R_{A} and a Solid metal sphere B of radius R_{B}( < R_{A})are kept far apart and each is given charge + Q. Now. They are connected by a thin metal wire. Then

Solution:

Electric field inside metal shell A is zero. After connecting A & B by thin metal wire, the charge will get redistributed such that both metal shell A and solid metal sphere B comes at same electric potential.

*Multiple options can be correct

QUESTION: 36

A Few electric field lines for a system of two charges Q_{1 }and Q_{2} fixed at two different points on the x - axis shown in the figure. These lines suggest that

Solution:

The number of lines of force emerging or converging at point charge depends on the magnitude of charge. Since the number of lines of force emerging from Q is greater than number of lines of force converging at Q_{2}.

Let electric field due to Q_{1} is and due to Q_{2}, is

To the left of are anti parallel, but E_{2} is always weaker than E_{1}

Since |Q_{2}| < |Q_{1}| and r_{2} > r_{1}

To the right of are antiparallel and

|Q_{1}| > |Q_{2}| but r_{1}> r_{2}

So at some point

and electric field will be zero.

*Multiple options can be correct

QUESTION: 37

Which of the following statement (s) is / are correct?

Solution:

If q_{1} and q_{2} are like charges then electric field between two point changes is zero somewhere. The workdone is moving a unit positive charge unaccelerated i.e. it remains in the state of quasistatic equilibrium which happens if force applied by external agency

*Multiple options can be correct

QUESTION: 38

Which one of the following statements regarding the electric field and is incorrect?

Solution:

W e know that electrostatic forces are given as negative of gradient of a potential i.e.;

Now in the given E F : -

Thus only E_{1} is electrostatic field.

Option A . B . D is the solution.

*Multiple options can be correct

QUESTION: 39

An electromagnetic wave propagates through a non-magnetic medium which has two parameters. These are dielectric constant, ε and refractive index n. Which relations are incorrect?

Solution:

In an Electromagnetic wave is propagated through a non - conducting magnetic medium of dielectric constant ε & of refracting index n then they are related as refractive index (n): -

then incorrect options are

*Multiple options can be correct

QUESTION: 40

If an electromagnetic wave is propagating in a medium with permittivity ε and permeability μ, then is the

Solution:

The ratio of E to H is intrinsic impedance of the medium

Thus from maxwell eq^{n}.

Therefore :- is called the intrinsic impedance of the medium.

*Answer can only contain numeric values

QUESTION: 41

Suppose that the electric Field on the xy plane is given by The magnitude of the difference in potential between the origin (0,0) and the point (1,2).

Solution:

*Answer can only contain numeric values

QUESTION: 42

A parallel plate capacitor is maintained at a certain potential difference. When a 3 mm thick slab is introduced b/w plates, in order to maintain the same Potential difference, the distance b/w the plates is increased by 2.4 m. The dielectric constant of the slab is __________.

Solution:

As here with introduction of slab or with change in separation, potential difference between the plates is changed, the charged capacitor is isolated, i.e., q = q'

So, C_{0}V_{0} = CV [as q = CV]

or, C_{0} = C [as V = V_{0} given]

Now as with introduction of dielectric slab the capacity increases from

by increasing d to (d + 0.24 cm) the capacity C_{1}, becomes

*Answer can only contain numeric values

QUESTION: 43

A parallel plate capacitor with plate area 40 cm^{2} and plate separation 5 mm is given a charge Q = 2 * 10^{-12}C. The battery is disconnected and a parallel faced dielectric slab (k = 5) of area 40 cm^{2} and thickness 3 mm is placed centrally between the two plates. What is the capacitance?

Solution:

The electric field due to the polarization charges is

The electric field inside the dielectric slab is

*Answer can only contain numeric values

QUESTION: 44

If the electrostatic potential at a point (x.y) is given by v = (2x + 4y) volts, the electrostatic energy density at that point is _____

Solution:

Electrostatic energy density =

*Answer can only contain numeric values

QUESTION: 45

Two long parallel wires Carrying current i are Separated by a distance 3a. There exists a square loop of side a with a capacitor of capacity C as shown in figure. The value of current varies with time as I = I_{0} sinωt. The maximum current in the square loop is given by as In4. Calculate the value of n.

Solution:

*Answer can only contain numeric values

QUESTION: 46

In figure, xy is an infinite line charge distribution. P and O are points as shown. The ratio of electric field at P and Q is a_{1}: a_{2} . Calculate the value of a_{1} +3a_{2}.

Solution:

The electric field due to an infinite line charge distribution at point P

and that is due to an infinite line charge distribution at point θ

Their ratio

*Answer can only contain numeric values

QUESTION: 47

The Circular are OTS is kept in an external magnetic field (2T) as shown in Figure. The arc carries a Current I (3 amp). The magnetic field is directed normal and into the page. Calculate the magnetic of force acting on the are.

Solution:

*Answer can only contain numeric values

QUESTION: 48

Figure shows two concentric coplanar coils with radius 10m and 20m. A current i = 2t flows in the smaller loop. Neglecting self inductance of larger loop. The emf induced in the larger coil is given by = Find the value of n.

Solution:

Magnetic field at the centre

emf induced in larger coil

*Answer can only contain numeric values

QUESTION: 49

Current density in an cylindrical coordinate in certain region is given as

The total current crossing the surface z = 3, r ≤ 6 in the direction is _____ A.

Solution:

*Answer can only contain numeric values

QUESTION: 50

Assuming the temperature and the molar mass of air. as well as the free-fall acceleration, to be independent of the height, find the difference in heights at which the air densities at the temperature 0^{0}C differ?

Solution:

we know that dp = - ρ gdh and from ideal gas constant temperature.

Integrating with in limits

*Answer can only contain numeric values

QUESTION: 51

The Electric field in a region of space is given by;

Calculate the flux due to this through an area 1 m2 lying in the y - z plane (in SI units)?

Solution:

*Answer can only contain numeric values

QUESTION: 52

A small magnetic dipole is kept at the origin in the x-y plane. One wire L_{1} is located at z = - a in the x-z plane with a current I flowing in the positive x-direction. Another wire L_{2} is at z = + a is y-z plane with the same current I as in L_{1} flowing in the positive y - direction. The angle made by the magnetic dipole with respect to the positive x-axis is ___________ (in degree).

Solution:

Resultant magnetic field at z = 0 makes an angle of 45° with - and 225^{0} with

*Answer can only contain numeric values

QUESTION: 53

A long solenoid, of radius a. is driven by alternating current, so that the field inside is Sinusoidal A circular loop of wire, of radius a/2 and resistance R, is placed inside the solenoid, and coaxial with it. Then the amplitude of current induced in the loop as a function of time is Then the value of α is _____.

Solution:

Magnetic flux through the loop

*Answer can only contain numeric values

QUESTION: 54

Assume that a lamp radiates 5W of power in free space uniformly in all directions. Then the magnitude of electric field strength (in V/m) at a distance 1 m from the lamp is ______ .

Solution:

*Answer can only contain numeric values

QUESTION: 55

An electromagnetic wave frequency 10 GHz is propagating through a conductor having conductivity 6 x 10^{7}(Ωm)^{-1}. Then skin depth of the conductor is ______

Solution:

skin depth

*Answer can only contain numeric values

QUESTION: 56

A plane electromagnetic wave traveling in free space is incident normally on a glass plate of refractive index 3/2. If there is no absorption by the glass, its transmissivity is____.

Solution:

*Answer can only contain numeric values

QUESTION: 57

The finite sheet on the z = 0 plane has a charge density Find the total charge on the sheet

Solution:

Since x dx= 1/2 d(x^{2}), we now integrate with respect to x^{2} (or change variables : x2 = u so that x dx = du/2).: x^{2} = u so that x dx = du/2).

*Answer can only contain numeric values

QUESTION: 58

Two condensers of capacitances 2μF and 3μF are charged to potentials 100 V and 200 V respectively. They are then joined in parallel in such a way that plates which have positive charges are connected together. The energy dissipated into heat in the process is_____.

Solution:

Then energy dissipation is given as

*Answer can only contain numeric values

QUESTION: 59

Find the force between a uniformly charged rod of length 4m with a charge 0.1 c and a point charge 1μc placed at a distance 4m from the centre of the rod at its axial position.

Solution:

*Answer can only contain numeric values

QUESTION: 60

Unpolarized light is incident on an air dielectric interface. The interface is the xy plane and the plane of incidence is yz plane. The electric field of the reflected light is given by

Where k is the propagation constant in air and ω is the angular frequency of the light. Assume magnetic permeability The dielectric constant of the second medium is ______

Solution:

Since reflected light is plane polarized, then angle of reflection is Brewster angle

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