Physics, asked by mannu9794, 3 months ago

magnetic field due to current through a very long circular cylinder​

Answers

Answered by savagekshiraj
1

If the current density as a function of distance 'r' from the axis of a radially symmetrical parallel stream of electrons is given as j(r)=

μ

0

xb(α+1)

r

α−1

if the magnetic induction inside the stream varies as B=br

α

, where b and α are positive constants. Find 'x'

Using Ampere's Circuital Law,∮

p

B.dl=μ

o

I (Equation 1)

Total current (I) flowing through the cross-section of radius r, I=∫

0

r

j(r

)×A

I=∫

0

r

μ

o

xb(α+1)(r

)

α−1

2πr

dr

I=

μ

o

xb(α+1)

2π∫

0

r

(r

)

α

dr

I=

μ

o

xb(α+1)

α+1

r

α+1

I=

μ

o

bx2πr

α+1

p

B.dl=∮

p

br

α

dl=br

α

p

dl

p

B.dl=br

α

2πr=2πbr

α+1

From equation 1 , 2πbr

α+1

o

μ

o

bx2πr

α+1

Hence, x=1

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