What is a displacement current? OPTIONS; a) a fictitious current across the plates of a capacitor b) charged particles moving in a changing magnetic field c) charged particle moving in a changing electric field d) the movement of the positive nuclei within atoms in response to a changing electric field e) the movement of the positive nuclei within atoms in response to a changing magnetic field
The correct answer and explanation is:
The correct answer is: a) a fictitious current across the plates of a capacitor.
Displacement current is a concept introduced by James Clerk Maxwell to complete Ampere’s Law. While Ampere’s Law initially described the relationship between electric current and the magnetic field, it had a limitation in the case of capacitors or situations where there was a time-varying electric field but no actual current. In such cases, Maxwell added the idea of displacement current to make the law applicable universally.
The displacement current arises when an electric field changes with time, such as between the plates of a capacitor during charging or discharging. Although there is no actual flow of charge across the plates, the changing electric field can still generate a magnetic field, just as a real current would. This imaginary current is known as the displacement current, and it accounts for the effects of a time-varying electric field.
In a capacitor, as the plates accumulate charge, the electric field between them changes over time. This changing electric field leads to the displacement current, which allows the capacitor to influence the surrounding magnetic field in a way similar to a conventional current.
Maxwell’s addition of displacement current made Ampere’s Law complete and accurate in describing electromagnetic phenomena. It helped unify the concepts of electricity and magnetism into the theory of electromagnetism. The displacement current is mathematically represented as: Id=ϵ0dΦEdtI_d = \epsilon_0 \frac{d\Phi_E}{dt}
Where IdI_d is the displacement current, ϵ0\epsilon_0 is the permittivity of free space, and dΦEdt\frac{d\Phi_E}{dt} is the rate of change of the electric flux through the capacitor’s plates.
This concept is fundamental in understanding the behavior of capacitors in alternating current circuits and in the propagation of electromagnetic waves.