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Homework Help: Magnetic field inside a cylinder with an offset hole

  1. Nov 21, 2016 #1
    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. jcsd
  3. Nov 21, 2016 #2
    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?
  4. Nov 21, 2016 #3


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