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

• A. $\frac{{\pi }^2}{4\sqrt{2}}$
  
• B. $\frac{{\pi }^2}{8\sqrt{2}}$
  
• C. $\frac{\pi }{2\sqrt{2}}$
  
• D. $\frac{\pi }{4\sqrt{2}}$

Answer 1

The correct option is B $\frac{{\pi }^2}{8\sqrt{2}}$




Magnetic field at the centre of circular coil $B_{circular}=\frac{{\mu }_0}{4\pi }.\frac{2\pi i}{r}=\frac{{\mu }_0}{4\pi }.\frac{4{\pi }^{2}i}{L}$
Magnetic field at the centre of square coil
$B_{square}=\frac{{\mu }_0}{4\pi }.\frac{8\sqrt{2}i}{a}=\frac{{\mu }_0}{4\pi }.\frac{32\sqrt{2}i}{L}$
Hence $\frac{B_{circular}}{B_{square}}=\frac{{\pi }^2}{8\sqrt{2}}$