Question

the magnetic field due to a current carrying circular loop of radius 3cm at a pt on the axis at a distance of 4cm from the center is 54micro T. what will b its value at center of loop?

Answer 1

$$\begin{gathered} Magneticfieldaytheaxis \\ B=\frac{{\mu }_{o}I{R}^2}{2(x^2+R^2{)}^{3/2}} \\ whereRistheradiusR=3cm \\ X=4cm \\ Magneticfieldatthecentre \\ {B}_c=\frac{{\mu }_{o}I}{2R} \\ \frac{B}{B_c}=\frac{\frac{{\mu }_{o}I{R}^2}{2(x^2+R^2{)}^{3/2}}}{\frac{{\mu }_{o}I}{2R}}=\frac{R^3}{(x^2+R^2{)}^{3/2}} \\ \frac{B}{B_c}=\frac{3^2}{(16+9{)}^{3/2}} \\ {B}_c=\frac{125}{27}B \\ {B}_c=250microtesla \end{gathered}$$