Displacement Current: Overview, Questions, Preparation

Jd​=ε0∂E/​∂t ​
Where,

Jd​ =  = displacement current

ε0 = free space

∂E/∂t = rate of change of electric field​

This topic is one of the crucial parts of the chapter electromagnetism and understanding its core concepts can help the candidates to tackle a wide range of numerical problems which are frequently asked in the JEE MAINS.

Ampere’s law is known to have various loopholes, such as in cases where there is a change in the electric fields over time. For example: a charging capacitor. When the electric current is flowing steady, there won’t be any issue. But as soon as there is a change in the flow of current, we observe that in this condition no conduction current flows through the dielectric between the plates. Therefore, the value of magnetic field should be nil.

However, that’s not the case. A substantial amount of magnetic field is noticed without any current flowing! To solve this issue, the concept of displacement current was introduced to avoid such confusions and fill the gaps set by the ampere’s law. How this change affected the flow of current is explained below for reference!

The general formula for ampere’s law can be denoted by:

∮B⋅dl=μ0​Ienc​
Where,

B= magnetic field

μ0= free space

Ienc = current enclosed by the loop

Due to the limitations in the old Amperes law, Maxwell suggested some changes in the original formula. This formula is now known as Ampere-Maxwell formula and is represented as:
B⋅dl=μ0​(Ienc​+ε0​dtdΦE​​)

Where,

ε0​dtdΦE​​ is the displacement current,

ΦEΦE​ is the electric flux.

This formula was successfully able to overcome the limitations of the existing Ampere’ law and could now be used in situations involving displacement current.

This Ampere-Maxwell equation proved to be a breakthrough for the field of electromagnetism due to several reasons, some of which are mentioned below:

• It overcomes the shortcomings of ampere’s law and ensured consistency with maxwell’s equation.
• Studying this helped to solve various queries related to electromagnetic waves, such as change in electric fields.
• Helped in explaining magnetic fields in capacitors.
• It allowed continuous flow of current despite the change in fields, such as areas where there is no flow of conduction current.