Question

Please Show Work Clearly.

12.3 Time-Harmonic Wave Equation. Using the source-free Maxwell's equations, show that a Helmholtz equation can be obtained in terms of the magnetic vector potential. Use the definition B = V X A and a simple medium (linear, isotropic, homogeneous material). Justify the choice of the divergence of A.

Answer 1

From the given data :

The Maxwell's equations fot the magnetic vectorcan be represented as the curl of some other vector

From Time-Harmonic wave Equation :- Using the source-free Medwellf Equation show that Helmholtz Equation can be obtained interme o magnetic Vector potential. Use the definetton B:XA and a simple medium (linear, isotropic, homogeneous material). Justify the choice of divergence of 'A' So): ot from the given Date: Madwell Equations are 1.J.D= ev 12.Do B o 3. DXE = -26 4. Ox H = OPED From the 2nd maxwelle Equation for magnetic vector potential CHHV. B=0} Divergence of a vector ile 0 (Zero) then & the vector is known at Solinoldal) Knowledge from the basic vector field The divergence of corl of any vector 4 Zero (O) 7.(0xĀ) : 06() le vxA iş a vector which is solinoidal from ew Of (2) we can write and Justify that B=(vx&A) Any Solino idal Vector can be represented as Corl of another Vector