The figure shows a cross section of a long cylindricalconductor of radius a = 2

Question

The figure shows a cross section of a long cylindricalconductor of radius a = 2 cm, carrying a uniformlydistributed current i = 10 A into the page. Evaluate B(x)at the values asked below. 1. B(x = 0.5 cm)?
(in T)
2. B(x = 1. cm)?
(in T)
3. B(x = 1.5 cm)?
(in T)
4. B(x = 2 cm)?
(in T)

5. B(x = 3 cm)?
(in T)

6. B(x = 4 cm)?
(in T)

7. B(x = 5 cm)?
(in T)

8. B(x = 6 cm)?
(in T)

The figure shows a cross section of a long cylindricalconductor of radius a = 2 cm, carrying a uniformlydistributed current i = 10 A into the page. Evaluate B(x)at the values asked below.

Explanation / Answer

from the Ampere's Law: i(r)*0=B(r)*2r i(r)=10*r2/a2 A =>r=0.5 cm  =>B(r)=2.5*10-5 T r= 1 cm => B(r)= 5*10-5 T r= 2 cm => B(r)=10-4 T for r>a cm B(r)=10*0/2r r= 4 cm=0.04 m=> B(r)=5*10-5 T r= 5 cm =0.05 m => B(r)=4*10-5 T r= 6 cm =0.06 m=> B(r)=3.33*10-5 T

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