# Magnetic field inside a cylinder with an offset hole

1. Nov 21, 2016

### oneofmany850

1. The problem statement, all variables and given/known data
Metal cylinder of radius a has the z-axis as its symmetry. It has magnetic field at any point P as: $$B[x,y,z] = \frac{1}{2} \mu_0 J_z [-ye_x + xe_y]$$

A cylindrical hole of radius b which is displaced from the cylinder's axis by d in the x direction. The magnetic field inside the hole is $$B = \frac{1}{2}\mu_0 J_z de_y$$

Does the field inside the hole make sense in the limit as d tends to zero? Explain why in 2 or 3 sentences.

2. Relevant equations

Deriving the field in the hole from the field in the cylinder using superposition gave, $$B = \frac{1}{2} \mu_0 J_z [-ye_x +xe_y + ye_x - [x-d]e_y]$$

3. The attempt at a solution

So as d tends to zero the axis of the hole is moving to the centre of the cylinder and just leaves us with $$B = \frac{1}{2} \mu_0 J_z$$? I'm not quite sure what the question is asking here. Any suggestions please?

2. Nov 21, 2016

### oneofmany850

Actually I think it shows that the magnetic field becomes zero in the hole when it is at the centre. Is this because of symmetry and cancelling?

3. Nov 21, 2016

Yes.