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A steady current flow in a long wire.it is bent into a circular loop of one turn and magnetic field at centre is B.if same wire is bent into a circular loop of n turns magnetic field at the centre of the coil is

A steady current flow in a long wire.it is bent into a circular loop of one turn and magnetic field at centre is B.if same wire is bent into a circular loop of n turns magnetic field at the centre of the coil is

Grade:12

2 Answers

Vikas TU
14149 Points
4 years ago
Hii 
Magnetic field at the centre of circle of radius a is 
B = mew *I/2a
If no, of turns increased 
Radius r = a/N 
No, of loops has also increased to N 
so, magnetic field at centre will be 
Bnew = mew * N*I/2r = mew * N2I/2a 
=> N2B
Khimraj
3007 Points
4 years ago

Here length of the wire is considered fixed. So the radius of the small turns r=R/N; where R the radius of the big circular loop.

then B=Mu_0* I/(2*pi*R)

and for the later case mag. field =Mu_0*I/(2*pi*(R/N))

=BN.

Edit1: But the current also increases N times so the ans is BN^2.

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