Question

An infinitely long circular cylinder carries a uniform magnetization parallel to its axis. Find the magnetic field inside and outside the cylinder

Answer 1

Answer: Outside of an indefinitely long solenoid, the magnetic field is zero.

In an indefinitely long solenoid, the magnetic field is equal to μ$_{0} Mk$.

Step-by-step explanation:

Step 1:

Consider a coordinate system S in which the z axis coincides with the axis of the cylinder. The magnetization of the material is equal to

$\bar M$$=Mk$

Since the material is uniformly magnetized, its bound volume current is equal to zero. The bound surface current is equal to

$\bar K_{b}$  $= \bar M * n$ $= \bar M * r$ = MФ

Step 2:

The current distribution in an endlessly long solenoid is equivalent to this current distribution.

Because the magnetic field outside an indefinitely long solenoid is zero, the field outside a magnetised cylinder will be zero as well. Using Ampere's law, we can simply determine the magnetic field within an infinitely long solenoid -

So the Magnetic field outside the cylinder is

$\bar B =$ μ$_{0}$$K_{b}$$k=$μ$_{0}$$Mk$

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