The ratio of the magnetic field at the centre of a current carrying circular wir

Question

The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

Options:

A . π24√2

B . π28√2

C . π2√2

D . π4√2

Answer: Option B
:
B

The Ratio Of The Magnetic Field At The Centre Of A Current C...

Magnetic field at the centre of circular coil

B_{c i r c u l a r} = \frac{μ_{0}}{4 π} . \frac{2 π i}{r} = \frac{μ_{0}}{4 π} . \frac{4 π^{2} i}{L}

Magnetic field at the centre of square coil

B_{s q u a r e} = \frac{μ_{0}}{4 π} . \frac{8 \sqrt{2} i}{a} = \frac{μ_{0}}{4 π} . \frac{32 \sqrt{2} i}{L}

Hence

\frac{B_{c i r c u l a r}}{B_{s q u a r e}} = \frac{π^{2}}{8 \sqrt{2}}

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