(NCERT) QUESTION & ANSWERS PHYSICS (Electromagnetic Waves)

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(Electromagnetic Waves)

1.  What do you mean by an electromagnetic wave?

  • Solution:
    Electromagnetic waves are by nature transverse to the direction of propagation of (i) oscillation of electric field and 
    (ii) oscillation of magnetic field, which are mutually perpendicular to each other. The direction of propagation of the wave is perpendicular to electric and magnetic fields.

 2.  Prove that only an accelerated charge can produce an electromagnetic wave.

  • Solution:
    A stationary charge has an electric field around it but no magnetic field. When given an impulse, it begins to move with the production of electric and magnetic fields. When the charge moves with a constant velocity, the magnetic field does not change with time, hence it cannot produce an electric field. As the charge is accelerated, both electric and magnetic fields change with time and space, one becoming a source of the other and giving rise to an electromagnetic wave.


 3.  What are the important properties of electromagnetic waves?

  • Solution:
    Some of the chief characteristics of electromagnetic waves are:
    (i) In an electromagnetic wave, the directions of oscillation of the electric and magnetic fields are perpendicular to  each other as well as to the direction of propagation of the wave.
    (ii) The speed of an electromagnetic wave in space is about 3 ´ 108 m/s while in any other medium, it depends on the electric and magnetic properties of the medium and not on the amplitude of the field variation.

    (iii) The electric and magnetic field variations are in phase, i.e. both attain their maxima and minima at the same rime and place.


4.  A parallel plate capacitor is being charged by an external source. Show that the sum of conduction current and displacement current has the same value everywhere in the circuit.


 5.  Check the dimensional consistency of Maxwell's equation and the Lorentz force law given below:
        Lorentz force law:


6.  Give a simple possibility argument to suggest that an accelerated change must emit electromagnetic radiation.

  • Solution:
    Let us consider a stationary electric charge. At some distance from this charge, there will be an electric field but no magnetic field. When the charge begins to move, there will be both electric and magnetic fields at P. If in a region of space, there is a flux of magnetic field varying with time, it gives rise to an emf (Faraday's law of electromagnetic induction). Applying this law to a small region, say a small square perpendicular to the direction of the magnetic field, it can be shown that the electric fields along the two parallel sides of the square are not the same. Thus a time dependent magnetic field gives rise to an electric field that varies with position. Now suppose that the electric field depends on time as well. Then from Maxwell's generalization of Ampere's circuital law, such an electric field produces a magnetic field. So, we find that electric and magnetic fields that depend on space and time produce and sustain each other. A simple form of such a continuing change is a wave. In a plane wave, for example, the electric and magnetic fields vary sinusoidally with distance at a given time, and with time at a given point. Thus, an oscillating charge, which has non-zero acceleration, will continuously emit electromagnetic waves.


 7.  A TV tower has height of 100m. How much population is covered by the TV broadcast if the average population density around the tower is 1000cm-2 ? (radius of the earth = 6.37 x 106m)


 8.  A capacitor made of two circular plates each of radius 12cm, and separated by 5.0 mm. The capacitor is being charged by an external source. The charging current is constant and equal to 0.15 A.
        (a) Calculate the capacitance and the rate of change of potential difference between the plates.
        (b) Obtain the displacement current across the plates.
        (c) Is Kirchoff's first role valid at each plate of the capacitor? Explain.


9.  Refer to the above, problem. Use Ampere law (modified to include displacement current) and the symmetry in the problem to calculate magnetic field between the plates at a point (i) on the axis,  (ii) 6.5 cm from the axis, and (iii) 15cm from the axis


 10.  A parallel plate capacitor of area 500cm2 and plate separation 3.0mm is charged initially to 80mC.Due to a radioactive source nearby, the medium between the plates gets slightly conducting and the plate loses charge initially at the rate of 1.5 x 10-8 Cs-1. What is the magnitude and direction of displacement current? What is the magnetic field between the plates?

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