Question

is the product BL remains same for an amperean loop for the given current?comment ​

Answer 1

Magnetic field at any point on Ampere's lop can be due to all currents passing through inside or outside the loop. But net contribution in the left hand side will come form inside current only.

For r<a current passing through within the cylinder of radius r is given by

∫

0

r

JdA=∫

0

r

kr

2

2πrdr=2πk∫

0

r

r

3

dr=kπr

4

/2

Now using Ampere's law:

B×2πr=μ

0

I=μ

0

kπr

4

/2⇒B=

4

μ

0

kr

3