3) An infinitely long, cylindrical conductor of radius R carries a current I with a non-uniform current density J = α r2 . α is a positive constant and r is the distance from the centre of the cylinder. a) Calculate the magnetic field at r ≤ R and r ≥ R. Work out the dot products, represent all the vectors with arrows. b) If the current is flowing along the z-axis of the cylinder, what is the direction of the magnetic field? Express your answer using a unit vector in cylindrical coordinates. c) Plot the magnitude of the magnetic field as a function of r.
3) An infinitely long, cylindrical conductor of radius R carries a current I with a non-uniform current density J = α r2 . α is a positive constant and r is the distance from the centre of the cylinder. a) Calculate the magnetic field at r ≤ R and r ≥ R. Work out the dot products, represent all the vectors with arrows. b) If the current is flowing along the z-axis of the cylinder, what is the direction of the magnetic field? Express your answer using a unit vector in cylindrical coordinates. c) Plot the magnitude of the magnetic field as a function of r.
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3) An infinitely long, cylindrical conductor of radius R carries a current I with a non-uniform current density
J = α r2
. α is a positive constant and r is the distance from the centre of the cylinder.
a) Calculate the magnetic field at r ≤ R and r ≥ R. Work out the dot products, represent all the vectors with
arrows.
b) If the current is flowing along the z-axis of the cylinder, what is the direction of the magnetic field? Express
your answer using a unit vector in cylindrical coordinates.
c) Plot the magnitude of the magnetic field as a function of r.
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