Question

You may recognize the figure below from an earlier homework. It, however, represents a very different physical situation: this is now a very long (infinite for our purposes) conducting wire in the form of a cylindrical shell. The inner radius of the shell a=3.5 mm and outer radius b=5.2 mm. The electric current I=10.5 A runs along this wire and is distributed uniformly throughout the shell cross-section. This current is the source of the magnetic field, which you will be evaluating. I 12 Find the magnitude of the magnetic field B(ri) inside the shell body at distance r1=4.86 mm from the cylindrical axis: Btr1)= G. Find the magnitude of the magnetic field B(r2) outside the shell body at distance ra=7.54 mm from the cylindrical axis: Br2)= G.

Answer 1

Here   permeabilty of free space.

Jo = 41 x 10-H/m

a)

b)

So now we get outside similarly, now consider outer amperian loop - a red. dotted circle of radius 8=82- asing B 8=82 and Iy=I in relation magnitude (B=B (82)) of magnetic field cylindrical shell at radial distance ra as, B(82) = Mo I 2 Trz Now using -3 82 = 7.54 mm = 7.54 x 10 m, I = 10.5 A get, B(82) = 44x10 x 10.5 2 * x 7.54 x 103 Mo=4IX 107 Him B(82) = 2-78 5X10 T -4 again asing -4 1G=10T we get B(%) = 2-785 & G So we have, magnitude of magnetic field 'Answer = B(8₂) = 2-79 G. Expressed at 8₂= 7-54 mm in three significant figures