Download Displacement current : Physics Assignment

History
In the middle of that century Maxwell struggled with the paradox of the capacitor, where charge entered one
plate and then flowed out of the other plate apparently without traversing the space between the plates. It
seemed that electric charge was being destroyed on one plate and being re-created when it reappeared on
the other plate. Maxwell postulated a new type of current, called "displacement current", as flowing across
the gap between the two plates so as to save the principle of continuity of electric current.
The displacement current
The calculation of the magnetic field of a current distribution can, in principle, be carried out using Ampere's
law which relates the path integral of the magnetic field around a closed path to the current intercepted by an
arbitrary surface that spans this path:
(1)
Ampere's law is independent of the shape of the surface chosen as long as the current flows along a continuous,
unbroken circuit. However, consider the case in which the current wire is broken and connected to a parallelplate capacitor (see Figure 1). A current will flow through the wire during the charging process of the capacitor.
This current will generate a magnetic field and if we are far away from the capacitor, this field should be very
similar to the magnetic field produced by an infinitely long, continuous, wire. However, the current intercepted
by an arbitrary surface now depends on the surface chosen. For example, the surface shown in Figure 1 does not
intercept any current. Clearly, Ampere's law can not be applied in this case to find the magnetic field generated
by the current.
Figure 1. Ampere's law in a capacitor circuit.
Although the surface shown in Figure 1 does not intercept any current, it intercepts electric flux. Suppose the
capacitor is an ideal capacitor, with a homogeneous electric field E between the plates and no electric field
outside the plates. At a certain time t the charge on the capacitor plates is Q. If the plates have a surface area A
then the electric field between the plates is equal to
(2)
The electric field outside the capacitor is equal to zero. The electric flux, intercepted by the surface shown in
Figure 1 is equal to
(3)
If a current I is flowing through the wire, then the charge on the capacitor plates will be time dependent. The
electric flux will therefore also be time dependent, and the rate of change of electric flux is equal to
(4)
The magnetic field around the wire can now be found by modifying Ampere's law
(5)
Where Φ E is the electric flux through the surface indicated in Figure 1 In the most general case, the surface
spanned by the integration path of the magnetic field can intercept current and electric flux. In such a case, the
effects of the electric flux and the electric current must be combined, and Ampere's law becomes
(6)
The current I is the current intercepted by whatever surface is used in the calculation, and is not necessarily the
same as the current in the wires. Equation (6) is frequently written as
(7)
Where Id is called the displacement current and is defined as
(8)
Properties of displacement Current
*for a steady electric field i.e. steady current the displacement current is zero
*for a charging capacitor the conduction and displacement current are equal and exist in different regions (
conduction current is present in the wire and same amount of displacement current is present between the plates
of a capacitor ).After the capacitor is fully charged the system again attains a steady state and displacement
current becomes zero
* In case of an A.C. the continuity of current is maintained across the plates of the capacitor as conduction
current through the conducting wires is the same as the displacement current across the plates
Differences between conduction and displacement current
Conduction current
Produced by flow of charges
Needs medium to move
Displacement current
Produced by variation of electric field in a
region
Can travel through vacuum
Electromagnetic waves
According to the faradays law a time varying magnetic field gives rise to an electric field and discovery of
displacement current proved that a time varying electric field can produce a magnetic field thus time dependent
electric and magnetic fields give rise to each other .These varying E and B fields travel through space and are
called Electromagnetic Waves
Source of EM Waves
An accelerated charged particle radiates EM Waves
Consider a chare oscillating with some frequency .This produces an oscillating electric field in space which
creates an oscillating magnetic field.
The frequency of the EM Wave naturally equals the frequency of oscillation of charge particle
Properties of EM Waves
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An electromagnetic wave moves or propagates in a direction that is at right angles to the vibrations of
both the electric and magnetic oscillating field vectors
The two fields are mutually perpendicular.
All electromagnetic waves transfer energy from one place to another are transverse waves can travel
through vacuum.
They DO NOT require any medium to travel from one point to another.
Travel through a vacuum at the speed of 3 x 108 m/s.
Obey wave properties like reflection and refraction.
Carry no electrical charge as they are neither positively nor negatively charged.
obey the wave equation: v = f.ƛ
The magnetic field oscillates in phase with the electric field. In other words, a wave maximum of the magnetic
field always coincides with a wave maximum of the electric field in both time and space.
10 The electric field is always perpendicular to the magnetic field, and both fields are directed at right-angles to
the direction of propagation of the wave. In fact, the wave propagates in the direction EXB. Electromagnetic
waves are clearly a type of transverse wave.
11 For a -directed wave, the electric field is free to oscillate in any direction which lies in the -y plane. The
direction in which the electric field oscillates is conventionally termed the direction of polarization of the
wave.
12 The maximum amplitudes of the electric and the magnetic fields are related via
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14 There is no constraint on the possible frequency or wavelength of electromagnetic waves. However, the
propagation velocity of electromagnetic waves is fixed, and takes the value
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