Question

Write maxwells equation for speed of electromagnetic waves

Answer 1

1. Gauss’ Law for electric fields:  

∫E→⋅dA→=q/ε0.

 (The integral of the outgoing electric field over an area enclosing a volume equals the total charge inside, in appropriate units.)

2. The corresponding formula for magnetic fields:

∫B→⋅dA→=0.

(No magnetic charge exists: no “monopoles”.)

3. Faraday’s Law of Magnetic Induction: 

∮E→⋅dℓ→=−d/dt(∫B→⋅dA→). 

The first term is integrated round a closed line, usually a wire, and gives the total voltage change around the circuit, which is generated by a varying magnetic field threading through the circuit.

4. Ampere’s Law plus Maxwell’s displacement current: 

∮B→⋅dℓ→=μ0(I+ddt(ε0∫E→⋅dA→)). 

This gives the total magnetic force around a circuit in terms of the current through the circuit, plus any varying electric field through the circuit (that’s the “displacement current