Derive Maxwell’s third equation in integral and differential form.

Given that D= 20x î +10 ĵ (C/m^{2} ). Determine the flux crossing 1 m^{2} area that is normal to the x-axis at x = 5m.

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Maxwell’s Third equation: Faraday’s law state that, electromagnetic force induced in a closed loop is negative rate of change of the magnetic flux. Faraday's law states that the EMF is also given by the rate of change of the magnetic flux:

Where = and ∅= If we have one surface ‘S’, then total magnetic flux over surface ‘S’ is

According to faraday’s law, induced magnetic flux is creates electric filed due charge flows
through the closed loop

According to Stokes theorem,

Using Equation (3) and Applying to eq. (1) & (2)

Both sides having same integration therefore
From equation (4)

Numerical::