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Question:

The expression of the electric field associated with an electromagnetic wave in vacuum is given by

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Determine the wave number, frequency, the direction of propagation and the magnitude and direction of the magnetic field associated with the wave.

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Question:

Using Maxwell’s equations in vacuum, derive the wave equation for the x-component of the electric field vector associated with an electromagnetic wave

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Question:

The diameter of a 3.0 m long solenoid is 0.80 m. The magnetic field at its centre is 0.80 T. Estimate the energy stored in the magnetic field of the solenoid.

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Question:

A wire loop of resistance 20  and radius 5.0 cm is kept in the plane of this paper in a changing uniform magnetic field B.  The direction of B  is perpendicular to the plane of the page and points out of it. If the magnitude of the induced current in the loop is 3.0 mA, determine the rate of change of the magnitude of the magnetic field B.

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Question:

ACCalculate the magnitudes of magnetic intensity H  and magnetic field B  at the centre of a 2500-turn solenoid which is 0.50 m long and carries a current of 1.0 A. $( \mu o = 4 \pi \times 10^{-7}Hm^{-1} )$

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Question:

A long, straight wire of diameter 2.0 mm carries a uniformly distributed current of 10 A. At what distance from the axis of the wire will the magnitude of B  be maximum? Justify your answer

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Question:

A 1.0 m length of current-carrying wire kept perpendicular to a magnetic field of magnitude 400 mT experiences a force of 3.0 mN. Determine the current flowing in the wire.

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Question:

A dielectric of dielectric constant 5.0 is filled in the gap between the plates of a capacitor. Calculate the factor by which the capacitance is increased, if the dielectric is only sufficient to fill up 1/5 of the gap.

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Question:

Define electric displacement vector D and deduce Gauss’s law for dielectrics.

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Question:

Derive the expression for electric potential due to a uniformly charged spherical shell at a point inside the shell.

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Question:

A non-conducting solid sphere of radius 2.0 m carrying net positive charge 20nC is enclosed by a concentric non-conducting thin spherical shell of radius 4.0 m carrying net negative charge 25nC. Determine the electric fields at the distances of 1.0 m, 3.0 m, and 10.0 m, respectively, from the centre of the sphere.

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Question:

Two positively charged particles each having charge 20 C, are kept at a distance of 2.0 m from each other. Determine the electric field due to each charge. Show the electric field vectors on an appropriate diagram.

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Question:

Using Gauss’ theorem, calculate the flux of the vector field $A = x^{3} i + x^{2} z j + yzk$ through the surface of a cube of side 2 units.

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Question:

Determine the work done by a force $F =xyj + yz j + xzk$ in taking a particle along the path defined by the equation $r (t) = t i + 2t^{2} j + t^{3} k ,0 \leq t \leq 1$ from $t = 0 to t=2$ Is the force conservative?