Question

Radius of current carrying coil is 'R'. The ratio of magnetic field at a axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil :-

• A. $⟮\frac{1}{2}{⟯}^{1/2}$
• B. $\frac{1}{2}$
• C. $⟮\frac{1}{2}{⟯}^{3/2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $⟮\frac{1}{2}{⟯}^{3/2}$

$\begin{array}{c}\overrightarrow{B}atRdis\tan ce=\frac{{\mu }_{o}I{R}^2}{2{\left(x^2+R^2\right)}^{3/2}}\\ =\frac{{\mu }_{o}I{R}^2}{2{\left(2R^2\right)}^{3/2}}\\ =\frac{{\mu }_{o}I{R}^2}{2.{\left(8\right)}^{1/2}.R^3}\\ =\frac{{\mu }_{o}i}{4\sqrt{2}R}\\ \overrightarrow{B}atcentre=\frac{{\mu }_{o}i}{2R}\\ Ratio=\frac{{\mu }_{o}i.2R}{4\sqrt{2}R.{\mu }_{o}i}=\frac{1}{2\sqrt{2}}={\left(\frac{1}{2}\right)}^{3/2}\\ Hence,\\ optionCiscorrectanswer.\end{array}$