An infinitely long conducting cylindrical rod of radius R1 carrying a current 3I

Question

An infinitely long conducting cylindrical rod of radius R1 carrying a current 3I as shown is surrounded by a concentric conducting cylindrical shell (also infinitely long) with a current I in the opposite direction as shown.

An infinitely long conducting cylindrical rod of radius R1 carrying a current 3l as shown is surrounded by a concentric conducting cylindrical shell (also infinitely long) with a current I in the opposite direction as shown. Find the magnitude of the magnetic field B(r) between the rod and the shell (R1 less than r less than R2). In this region, what is the the direction of H at a point P directly above the axis of the rod? Find the magnitude of the magnetic field B(r) outside the shell (r greater than R2). In this region, what is the direction of B at a point P directly above the axis?

Explanation / Answer

1) by gauss law

B.dL = Mu*Ienc

I enclosed = 3I here

so

2pi*r*B = Mu*3I

B =  Mu*3I/2pi*r

counterclockwise

b)

similerly

I enclosed = (3I-I) here

so

2pi*r*B = Mu*(3I-I)

B =  Mu*2I/2pi*r

= Mu*I/pi*r

counterclockwise

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