: QUESTION & ANSWERS PHYSICS
1. What do you mean by an
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.
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?
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.
Consider a parallel plate capacitor. If the plates of the
capacitor have an area A, and a total change Q, the magnitude of the
between the plates is e0.
The electric flux E between the plates is
If Q on the capacitor plate changes with time, there is a current I = ,
so that we have
Then if we generalize Ampere's circuital law by adding to the total
current carried by conductors through the surface, another term which is e0
times the rate of change of electric flux through the same surface, the
total has the same value I for all surfaces. Therefore
at a point outside the plates is nearly the same as at a point just
inside as it should be. The first current, carried by conductors and due
to flow of charges is called conduction current. The second is due to
changing electric field or electric displacement is called displacement
current. By Maxwell's generalization it is not just the conduction
electric current due to flowing charges, but also the time rate of change
of electric field. More precisely, the total current I is equal to Ic,
conduction current plus Id, the displacement current
i.e. I = Ic +Id
The displacement current is e0
times the rate of change of flux of electric field through the same
surface as that through which the flow of conduction current is
calculated. Therefore in all respects, the displacement current has the
same physical effects on the conduction current.
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
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
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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