The magnetic field due to a current carrying circular loop of radius 6 cm at a point on the axis at a distance of 8 cm from the centre is \(216 \mu J\) Then magnetic field at the centre of the ring is \(\mu T\).

B
\(B_{(\text {Axis })}=\frac{\mu_0 I a^2}{2\left(a^2+x^2\right)^{\frac{3}{2}}}\)
and
\(B_{\text {Centre }}=\frac{\mu_0 I}{2 a}\)
\(\begin{array}{l}\therefore \frac{ B _{\text {Centre }}}{ B _{\text {Axis }}}=\frac{\mu_0 I }{2 a} \times \frac{2\left(a^2+x^2\right)^{\frac{3}{2}}}{\mu_0 I a^2} \\ \therefore \frac{B_{\text {Centre }}}{ B _{\text {Axis }}}=\frac{\left(a^2+x^2\right)^{\frac{3}{2}}}{a^3} \\ \therefore \frac{B_{\text {Centre }}}{ B _{\text {Axis }}}=\frac{\left(6^2+8^2\right)^{\frac{3}{2}}}{(6)^3}=\frac{(100)^{\frac{3}{2}}}{216} \\ \therefore \quad \frac{B_{\text {Centre }}}{ B _{\text {Axis }}}=\frac{\left(10^2\right)^{\frac{3}{2}}}{216} \\ \therefore \quad \frac{B_{\text {Centre }}}{216 \mu T}=\frac{1000}{216}=\frac{1000}{216} \\ \therefore \quad B_{\text {Centre }}=1000 \mu T\end{array}\)