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2) In free space, where A represents the magnetic potential vector and B represents the magnetic field vector. Prove that AA=-curl (B), with A is the Laplacian operator.

2) In free space, where A represents the magnetic potential vector and B represents the magnetic field vector. Prove that AA=-curl (B), with A is the Laplacian operator.

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Exercise 3: 1) A magnetic potential vector A is given in the cylindrical coordinates system (up,uo,k) by the relation A=5 psin (g)k. Prove that its associated magnetic field is given in cartesian coordinates system (i, j,k) by the relation B =5i. 2) In free space, where represents the magnetic potential vector and B represents the magnetic field vector. 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 the scalar magnetic potential), deduce that Vm verify Laplace equation.
Transcribed Image Text:Exercise 3: 1) A magnetic potential vector A is given in the cylindrical coordinates system (up,uo,k) by the relation A=5 psin (g)k. Prove that its associated magnetic field is given in cartesian coordinates system (i, j,k) by the relation B =5i. 2) In free space, where represents the magnetic potential vector and B represents the magnetic field vector. 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 the scalar magnetic potential), deduce that Vm verify Laplace equation.
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