A long wire of radius 2a is constructed as shown with a cylindrical cavity of ra

Question

A long wire of radius 2a is constructed as shown with a cylindrical cavity of radius a along its entire length. A current I flows in the positive z-direction (that is, out of the page). What is the current density I in the wire? What is the magnetic field at (0, 0)? (Hint: Replace the cavity with a solid wire having current density -I z and another having current density - 2.) What is the magnetic field at (a, 0)? Derive an expression for the magnetic field at all points along the x-axis. What is the magnetic field at (a, a)?

Explanation / Answer

a) I/S where S=pi*(2a)^2-pi*a^2=3pi*a^2. so J=I/(3pia^2) b) replace like the hint. we have. B*2pi*a=-J*pi*a^2*muy0 so B=-J*muy0*a/2 c) B1=-J*muy0*2a/2 B2=-J*muy0*a/2. so B'=B2-B1=-J*muy0*a/2 d). just consider x>a and x

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