Maxwell’s Equations Solved Examples
Let’s solve some example problems on Maxwell’s Equations:
Example 1: In an electromagnetic wave, the electric field of amplitude 5.4 V/m oscillates with a frequency of 3.0 x 1010 Hz. Calculate the energy density of the wave.
Solution:
The amplitude of the electric field, E0 = 5.4 V/m
Frequency of the electric field, f = 3.0 × 1010 Hz
According to Maxwell’s equations, energy density is given by
Energy density = ∈0E02
Where
∈0 is the absolute permittivity of the free space = 8.854 × 10-12 C2N/m2
E0 is the amplitude of the electric field
On substituting the values, we get
Energy density = (8.854 x 10-12 ) × (5.4)2
Energy density = 2.58 × 10-10 J/m3
Example 2: If the velocity of a charged particle in perpendicular electric and magnetic field is 7.5 X 106m/s and the Electric field is 4 X 106 N/c, what should be the value of magnetic field for velocity sector?
Solution:
As we know, for velocity selector, v = E / B
Therefore, B = E/v
⇒ B = 4 × 106 /7.5 × 106
⇒ B = 0.53 T
Example 3: A point charge of 10-6 C is at the centre of a cubical Gaussian surface of sides 0.5 m. What is the flux for the surface?
Solution:
We know that for a Gaussian surface, flux = q/ε
Here, q = 10-6 C and ε = 8.85 × 10-12 C/Nm2
Therefore, flux = 10-6/8.85 × 10-12
= 1.12 × 105 Nm2/C.
Maxwell’s Equations in Electromagnetism
Maxwell’s Equations are a set of four equations proposed by mathematician and physicist James Clerk Maxwell in 1861 to demonstrate that the electric and magnetic fields are co-dependent and two distinct parts of the same phenomenon known as electromagnetism.
These formulas show how variations in the quantity or velocity of charges can impact magnetic and electric fields. Maxwell went on to establish that light is an electromagnetic wave caused by oscillations in the electric and magnetic fields. Maxwell’s equations give a mathematical model for the operation of all electronic and electromagnetic devices, ranging from power generation to wireless communication.
Table of Content
- What are Maxwell’s Equations of Electromagnetism?
- Maxwell’s First Equation
- Maxwell’s Second Equation
- Maxwell’s Third Equation
- Maxwell’s Fourth Equation
- Applications of Maxwell Equations