Exercise 3:1) A magnetic potential vector A is given in the cylindrical coordinates system (up,uo,k) by therelation A=5 psin (g)k. Prove that its associated magnetic field is given in cartesian coordinatessystem (i, j,k) by the relation B =5i.2) In free space, whererepresents the magnetic potential vector and B represents the magnetic fieldvector. Prove that AA=-curl (B), with A is the Laplacian operator.3) Consider that the magnetic field vector is given by the relation B =-HoV Vm (Vm represents thescalar magnetic potential), deduce that Vm verify Laplace equation.

Given: The magnetic vector potential in cylindrical polar coordinates is A→ = 5 ρ sinϕ k→ To prove:…

Answered: 1) A magnetic potential vector A is…

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1) A magnetic potential vector A is given in the cylindrical coordinates system (up,uo,k) by the relation A=5 psin (9)k. Prove that its associated magnetic field is given in cartesian coordinates system (i, j,k) by the relation B=5i.