Question

A wire of length land earning current I is shaped into a circular coil of one turn and radius R. How will the magnetic field at the center of this current carrying circular coil change if the same wire is shaped into a coil of n turns now.

Answer 1

Answer:

Area of the coil initially A=πR

2

∴ Initial magnetic moment μ=NIA=NI(πR

2

)

Length of the coil initially L=N(2πR)

Radius of new coil formed R

′

=

2

R

Let the number of turns in new coil be N

′

.

But the length of the new coil formed must be equal to that of original coil i.e L

′

=L

∴ N

′

×2π

2

R

=N×2πR ⟹N

′

=2N

Thus area of new coil A

′

=

4

πR

2

∴ Magnetic moment of new coil μ

′

=N

′

IA

′

=2NI×

4

πR

2

=

2

NIπR

2

⟹

μ

μ

′

=

2

1