Faraday’s Law Notes & Topics for GATE EE/IES/ISRO/BARC 2019

By BYJU'S Exam Prep

Updated on: September 25th, 2023

In this article, you will find the Study Notes on Faraday’s Law which will cover the topics such as Introduction & some key points related to it.

A time varying magnetic field produces an electromotive force (or emf) which may establish a current in a closed circuit,

10-Faradays-Law (1)

For transformer,

10-Faradays-Law (2)

and for motional emf, 10-Faradays-Law (3)

where u is called energy density

* Displacement Current

10-Faradays-Law (4)

where 10-Faradays-Law (5) is known as displacement current density.

* Time harmonic fields are those that vary sinusoidally with time

10-Faradays-Law (6)

* In a Lossy, charge free medium, the wave equation based on Maxwell’s equation is of the form.

10-Faradays-Law (7)

Loss Tangent

10-Faradays-Law (8)

Where, 10-Faradays-Law (9) is complex permittivity.

For lossless dielectric 10-Faradays-Law (10) for good conductors 10-Faradays-Law (11) and for lossy dielectric loss tangent 10-Faradays-Law (12) is of the order of unity.

Reciprocal of attenuation constant is known as skin depth or penetration depth. It measures the depth at which field intensity reduces to the electron of the original value.

Skin depth 10-Faradays-Law (13)

For good conductor

10-Faradays-Law (14)

The Poynting vector P is the power flow vector whose direction is the same as the direction of wave propagation.

P = E × H

10-Faradays-Law (15)

* If a plane wave is an incident normally from medium 1 to medium 2, the reflection and transmission coefficients are given as,

10-Faradays-Law (16)

and transmission coefficient

10-Faradays-Law (17)

* The standing wave ratio is defined as

10-Faradays-Law (18)

* Intrinsic Impedance 10-Faradays-Law (19)

10-Faradays-Law (20)

* 1 Np = 20 log10 e = 8.69 dB

Key Points

* Free space

σ = 0, ε = ε0, μ = μ0

* Lossless dielectrics

σ = 0, ε = εrε0, μ = μrμ0 or σ << ωε

* Lossy dielectrics

σ ≠ 0, ε = εrε0, μ = μrμ0

* Good conductors

σ = ∞, ε = ε0, μ = μrμ0 or σ << ωε

Where σ is conductivity, ε is permittivity and μ is permeability of medium.

All the Best.

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