Physics - Magnetism Question with Solution | TestHub

Magnetic field at the centre

$b=\frac{{\mu }_0\text{I}}{2c}\otimes +\frac{{\mu }_0\text{I}}{2b}\left(\frac{3}{4}\right)\odot +\frac{{\mu }_0\text{I}}{2a}\left(\frac{3}{4}\right)\otimes$

As per problem :

$0=\frac{{\mu }_0\text{I}}{2}\left[\frac{1}{c}-\frac{3}{4b}+\frac{3}{4a}\right]\Rightarrow \frac{3}{4}\left[\frac{1}{b}-\frac{1}{a}\right]=\frac{1}{c}$

If$c=2a,$

$\frac{3}{4}\left[\frac{1}{b}-\frac{1}{a}\right]=\frac{1}{2a}\Rightarrow a=\frac{5}{3}b$