A long metal cylinder of radius (a) has the z-axis as its axis of symmetry. The cylinder carries a steady current of uniform current density
(Vector)J=(J subscript (z)) ((vector)e subscript(z)).
Derive an expression for the magnetic field at distance r from the axis where r
By resolving the cylindrical unit (vector)e subscript (phi) along the x and y axes, show that the magnetic field at any point P inside the cylinder is
vectorB(x,y,z)=( ((miu) (subscript o))/2 )J subscript z (-ye subscript x +x (vector)e(subscript)y)
where P has the Cartesian coordinates (x,y,z) and (x^2 +y^2)
Part B
A cylindrical hole of radius b,a is drilled through the cylinder.The axis of the hole is parallel to the axis of the cylinder,but is displaced from it by a distance d in the x-direction where dvectorJ=J subscript z *vector e subscript z
throughout the remaining material of the cylinder, and there is no current in the hole.
Use the result of part (a) to show that the magnetic field inside the cylindrical hole is uniform by the expression B=((miu) subscript 0)/2*(J subscript z)* d*(vector e subscript y )