Magnetic Flux Density in a Circular Loop

[leena19]

Homework Statement

A current flows in a circular loop consisting of a single turn.If the same wire is bent into a circular loop of 2 turns and the same current is passed through the loop,the magnetic flux density at the centre will change by a factor of ...?
(ans: 4 )


Relevant equations

B = (mu0 * N*I)/2r

The attempt at a solution

For the 1st loop,
B = (mu0 *I)/2r

To find B' after bending,
the length of the wire remains unchanged = 2*pi*r
so to form 2 circular loops the radius has to be halved for each loop?
which makes
B' = (mu0 * N*I)/(2r/2)
B' = (mu0 * 2*I)/(r) ?

so change in flux = B-B'/B
= 3
Thanks in advance.

 

[rl.bhat]

flux density at the centre will change by a factor of ...?
Chang by factor means you have to take the ratio, not the difference.
In the problem n will be doubled and r reduces to half.

 

[leena19]

Oh I get it now.
Thank you very much!