Physics Topics are also essential for space exploration, allowing scientists to study phenomena such as gravitational waves and cosmic rays.
Does Displacement Current Create Magnetic Field? Define Electromagnetic Wave?
In 1865, James Clerk Maxwell analysed the nature of light. According to him, light is a progressive wave of an electric and a magnetic field. In other words, light is an electromagnetic wave. At this time, except visible light, infrared and ultraviolet, the exis-tence of other electromagnetic waves was unknown.
As per Maxwell’s electromagnetic theory, an electric field and a magnetic field exist at each point on the path of propagation of an electromagnetic wave. These two fields undergo periodic vibrations. These vibrations propagate from one point to the next, and thus electromagnetic wave spreads. Electric and mag-netic fields can spread in all directions even without any material medium (solid, liquid or gaseous). Hence, electromagnetic waves can propagate in vacuum also.
Displacement Current
As per Ampere’s circuital law (See chapter ‘Electromagnetism,’ section 1.5),
\(\oint \vec{B} \cdot d \vec{l}\) = µ0I …… (1)
But the law has a limitation. What would be the form of the above equation for a varying current I, i.e., for a varying electric field inside a conductor, is not mentioned. For example, during the charging of a capacitor, varying current flows through the cir-cuit though no current flows in between the plates of the capac-itor. Equation (1) is not applicable in such cases. Maxwell corrected this error by adding another term to the right side of equation (1). This additional term is,
µoId = µoεo …. (2)
Maxwell mentioned the quantity Id as displacement current. Note that there is no valid reason for using the word ‘displace-ment’ in this context. But, the word is entrenched in the language of physics.
εo and ϕE(=\(\int \vec{E} \cdot d \vec{A}\)) in equation (2) are the permittivity of free space and electrical flux through a Gaussian surface respectively.
Therefore, \(\frac{d \phi_E}{d t}\) is the rate of change of electrical flux and clearly, Id = \(\epsilon_0 \frac{d \phi_E}{d t}\) is the expression representing varying electrical field. This varying electrical field is equivalent to the current flow between the plates of the capacitor during charging (known as displacement current). So, now there is no discontinuation in current flow. Hence, the general form of Ampere’s circuital law is,
\(\oint \vec{B} \cdot d \vec{l}\) = µ0I + µ0ε0\(\frac{d \phi_E}{d t}\) …… (3)
which is also known as Ampere-Maxwell law.
The meaning of this expression can be understood with the help of Fig. The electric flux through surface S2 is
ϕE = \(\int \vec{E} \cdot d \vec{A}\) = EA, where A is the area of the capacitor plates and E is the magnitude of the uniform electric field between the plates. If Q is the charge on the plates at any instant, then
E = \(\frac{Q}{\epsilon_0 A}\) (see chapter ‘Capacitance and Capacitor’).
Therefore, ϕE = EA = \(\frac{Q}{\epsilon_0}\)
Hence, the displacement current through S2 is
Id = \(\epsilon_0 \frac{d \phi_E}{d t}\) = \(\frac{d Q}{d t}\)
Clearly, the displacement current through S2 is exactly equal to the conduction current I through S1.
The displacement current can be identified as the source of the magnetic field on the surface S2. The displacement current has its physical origin in the time-varying electric field. The central point of this formalism is that magnetic field can be produced in two ways—if
- current flows through a conductor or
- electric field varies with time in a region.
The general form of Faraday’s law of induction is,
\(\oint \vec{E} \cdot d \vec{l}\) = \(-\frac{d \phi_B}{d t}\)
It can be concluded from this law that, a changing magnetic field creates an electric field (that is an emf in a conductor). Similarly, from the above law, we can conclude that a changing electric field sets up a magnetic field. In other words, the concept of dis-placement current develops an important connection between varying electric field and magnetic field. These varying electric and magnetic fields spread out in all directions and is known as electromagnetic waves.
Definition: When varying electric and magnetic field exist in a place then these varying fields spread out in all directions like a wave which is called electromagnetic wave.