3- In class, we introduced the vector potential Ä to write the magnetic field B as B = V × Ã. We showed that we could always choose Ä to satisfy V · Ã = 0. Using Ampére's law, we then found %3D j(F") dr' ÃF) = Но %3D 4т for a localized (volume) current density. a) Verify that this vector potential Ã(7) indeed satisfies ỹ ·Ã = 0. b) Verify that the magnetic field B is consistent with Biot-Savart's law. c) Finally, verify also that Ampére's law follows automatically from this vector potential Ā(7).
3- In class, we introduced the vector potential Ä to write the magnetic field B as B = V × Ã. We showed that we could always choose Ä to satisfy V · Ã = 0. Using Ampére's law, we then found %3D j(F") dr' ÃF) = Но %3D 4т for a localized (volume) current density. a) Verify that this vector potential Ã(7) indeed satisfies ỹ ·Ã = 0. b) Verify that the magnetic field B is consistent with Biot-Savart's law. c) Finally, verify also that Ampére's law follows automatically from this vector potential Ā(7).
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Transcribed Image Text:3- In class, we introduced the vector potential Ä to write the magnetic field B as B = V × Ã. We
showed that we could always choose Ä to satisfy V · Ã = 0. Using Ampére's law, we then found
%3D
j(F")
dr'
ÃF) =
Но
%3D
4т
for a localized (volume) current density.
a) Verify that this vector potential Ã(7) indeed satisfies ỹ ·Ã = 0.
b) Verify that the magnetic field B is consistent with Biot-Savart's law.
c) Finally, verify also that Ampére's law follows automatically from this vector potential Ā(7).
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