An air filled cylindrical capacitor (capacitance ) of length , with  and  as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity  is inserted inside  of the annular region as shown in Fig. (ii). The value of  for which the capacitance of the capacitor in Fig. (ii), becomes  is

Consider two coupled circuits, having self-inductances  and , that carry nonzero currents  and , respectively. The mutual inductance between the circuits is  with unity coupling coefficient. The stored magnetic energy of the coupled circuits is minimum at which of the following value(s) of  ?

The given equation represents a magnetic field strength  in the spherical coordinate system, in free space. Here,  and  represent the unit vectors along  and , respectively. The value of  in the equation should be ________ (rounded off to the nearest integer).        

In the figure, the electric field  and the magnetic field  point to  and  directions, respectively, and have constant magnitudes. A positive charge '  ' is released from rest at the origin. Which of the following statement(s) is/are true.

An infinite surface of linear current density  exists on the  plane, as shown in the figure. The magnitude of the magnetic field intensity  at a point  due to the surface current in Ampere/meter is __________ (Round off to 2 decimal places).

A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is  for the region r < b where r is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for r < b) is

If the magnetic field intensity (H) in a conducting region is given by the expression, . The magnitude of the current density, in , at 𝑥 = 1 m, 𝑦 = 2 m, and 𝑧 = 1 m, is

Which one of the following vector functions represents a magnetic field ? (, and  are unit vectors along x-axis, y-axis, and z-axis, respectively)

One coulomb of point charge moving with a uniform velocity enters the region x ≥ 0 having a magnetic flux density

. The magnitude of force on the charge at  is ________ N.

( and  are unit vectors along x-axis, y-axis, and z-axis, respectively.)

A conducting square loop of side length 1 m is placed at a distance of 1 m from a long straight wire carrying a current I = 2 A as shown below. The mutual inductance, in nH (rounded off to 2 decimal places), between the conducting loop and the long wire is __________.

A transformer with toroidal core of permeability  is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius, and neglecting any leakage flux, the best estimate for the mean radius R is

A solid iron cylinder is place in region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

The magnitude of magnetic flux density (B) in micro Teslas (µT), at the center of a loop of wire wound as a regular hexagon of side length 1 m carrying a current (I = 1 A) and placed in vacuum as shown in the figure is _________. (Give the answer up to two decimal places).

A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the relative permeability  of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent points located just inside and just outside the toroid, is _____________.

The flux linkage  and current (i) relation for an electromagnetic system is . When  I = 2A and g (air-gap length) = 10 cm, the magnitude of mechanical force on the moving part, in N, is ________________.

A rotating conductor of 1 m length is placed in a radially outward (about the z-axis) magnetic flux density ((B) of 1 Tesla as shown in the figure below. Conductor is parallel to and at 1 m distance from the z-axis. The speed of the conductor in r.p.m. required to induce a voltage of 1V across it, should be ___________.

Consider a one – turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the loop is perpendicular to the field lines. The resistance of the loop is  and its inductance is negligible. The magnetic flux density (in Tesla) is a function of time, and is given by B(t) =0.25sin , where radian/second. The power absorbed (in Watt) by the loop from the magnetic field is

A steady current I is flowing in the –x direction through each two infinitely long wires at  as shown in the figure. The permeability of the medium is. The -field at (0, L, 0) is

A circular turn of radius 1m revolves at 60rpm about its diameter aligned with the x – axis as shown in the figure. The value of  is  is SI unit. If a uniform magnetic field intensity  A/m is applied, then the peak value of induced voltage, (in Volts), is _____________.

The following four vector fields are given in Cartesian co – ordinate system. The vector field which does not satisfy the property of magnetic flux density is

The magnitude of magnetic flux density  at a point having normal distance d meters from an infinitely extended wire carrying current of I A is  (in SI units). An infinitely extended wire is laid along the x-axis and is carrying current of 4A in the +ve x direction. Another infinitely extended wire is laid along the y-axis and is carrying 2A current in the +ve direction. is permeability of free space. Assume  to be unit vectors along x, y and z axes respectively

Assuming right handed coordinate system, magnetic field intensity,  at coordinate (2,1,0) will be

The flux density at a point in space is given by. The value of constant k must be equal to        

A coil of 300 turns is wound on a non-magnetic core having a mean circumference of 300 mm and a cross-sectional area of
 . The inductance of the coil corresponding to a magnetizing current of 3A will be

(Given that)

Which of the following statements holds for the divergence of electric and magnetic flux densities

Consider the following statements with reference to the equation                          

(1) This is a point format the continuity equation

(2) Divergence of current density is equal to the decrease of charge per unit volume per unit at every point

(3) This is Maxwell’s divergence equation

(4) This represents the conservation of charge

Select the correct answer

The inductance of a long solenoid of length 1000 mm wound uniformly with 3000 turns on a cylindrical paper tube of 60mm diameter is          

Two conductors are carrying forward and return current of +I and –I as shown in Figure.  The magnetic field intensity at point P is

Two infinite strips of width w m in x direction as shown in Figure, are carrying forward and return currents of +I and –I in the z direction. The strips are separated by a distance of x m. The inductance per unit length of the configuration is measured to be L H/m. If the distance of separation between the strips is now reduced to , the inductance per unit length of the configuration

The magnetic vector potential in a region is defined by.  An infinitely long conductor, having a cross section area,
 and carrying a dc current, I = 5A in the y direction, passes through this region as shown in Figure.

Determine the expression for (a)  and (b) force density  exerted on the conductor.

An electron with velocity u is placed an electric field E and magnetic field B. the force experienced by the electron is given by

(a) For the construction of a suitable Gaussian surface, the capacitance of a spherical capacitor consisting of two concentric shells of radii a and b is given by = ?

(b) A current I in the short conducting element shown in fig produces a flux density  at point 1.

Determine the magnitude and the direction of

the flux density vector at point 2.

Two parallel wires separated by a distance d are carrying a current I in the same direction. The magnetic field along a line running parallel to these wires and midway between them

An electromagnetic field is radiated from

The laws of electromagnetic induction (Faraday’s and Lenz’s law) are summarized in the following equation:

An electron moves in the X-Y plane with a speed of . Its velocity vector makes an angle of  with X-axis. A magnetic field of magnitude  T exists along the Y-axis. Compute the magnetic force exerted on the electron and its direction.

An infinitely long straight wire carries 1000A of current and in the vicinity there is a circular conducting loop of 100mm diameter with the center of the loop 1m away from the straight conductor. Both the wire and the loop are coplanar. Determine the magnitude and direction of current in the loop that produces a zero flux density at its center.

A square coil of turns and 10cm side is moved through a steady magnetic field of  at a constant velocity of 2m/sec with its plane perpendicular to the field as shown in figure. Plot the variation of induced e.m.f as the coil moves along the field.

The energy stored in the magnetic field of solenoid 30 cm long and 3 cm diameter wound with 1000 turns of wire carrying a current of 10A is

A monochromatic plane electromagnetic wave travels in vacuum in the positive X direction (x, y, z system of coordinates). The electric and magnetic fields can be expressed as

A steady current I flows through a long cylindrical wire of radius R. find the magnetic vector potential at any point outside the conductor at radius. Vector potential on the surface of the conductor may be taken to be equal to zero.

When a transformer winding suffers a short-circuit, the adjoining turns of the same winding experience

Static magnetic fields induce currents in closed conducting loops. ( True=1, False=0)

Match the appropriate item from the right-hand side with those on the left-hand side.         

The inductance of a coil is proportional to the Cube of the number of turns, all over parameters remaining the same. (True=1, False=0)

The line integral of the vector potential A around the boundary of a surface S represents