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  • A infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length . The magnitude of the magnetic field (B) as a function of r

A infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length . The magnitude of the magnetic field (B) as a function of radial distance r from the axis is 

Option: 1


Option: 2


Option: 3


Option: 4


Answers (1)

best_answer

As we have learned

Magnetic field outside the thick hollow cylinder -

 

B_{surface}=\frac{\mu_{o}i}{2\pi R}

 

 

 

 

r = dis . of point from centre 

r < R/2  use Ampere's Law 

\oint B de= \mu _0 I

B \times 2\pi r = \mu _0 I\Rightarrow B= \frac{\mu _0}{2 \pi}\times I/r\;\; \; if\; \; \; r= R

Since inside = 0 

B = 0

B = \frac{\mu _0I}{2 \pi R}

For \frac{R}{2}\leq r \leq R

I = [ \pi r^2 - \pi [R/2]^2]\sigma \; \; \; \; \; \; \; \; \; \; \sigma = I/A

B = \frac{\mu _0\sigma }{2r}[r^2-\frac{R^2}{4}]

at r=R 

B = 3/8 \mu _0 \sigma R

B = \mu _0/2 \pi \times I/r

B \propto \frac{1}{r}

 

 

 

 

 

 

 

 

 

Posted by

avinash.dongre

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