# Magnetic field inside a cylinder with an offset hole

## Homework Statement

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.

## Homework Equations

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

## The Attempt at a Solution

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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?

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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?

TSny
Homework Helper
Gold Member
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?
Yes.