Two circular loops A and B , each of radius $\displaystyle 3$ m , are placed coaxially at a distance of $\displaystyle 4$ m . They carry currents of $\displaystyle 3$ A and $\displaystyle 2$ A in opposite directions respectively. Find the net magnetic field at the centre of loop A .

\[\begin{aligned} \mathrm{B}_{1} & =\frac{\mu_{0} I}{2 r} \\ \mathrm{B}_{1} & =\frac{4 \pi \times 10^{-7} \times 3}{2 \times 3}=2 \pi \times 10^{-7} T=6.28 \times 10^{-7} T \\ \mathrm{B}_{2} & =\frac{\mu_{0} I R^{2}}{2\left(R^{2}+x^{2}\right)^{3 / 2}} \\ & =\frac{2 \pi \times 10^{-7} \times 2 \times 9}{\left(3^{2}+4^{2}\right)^{3 / 2}} \quad, \text { opposite to } \mathrm{B}_{1} \\ \mathrm{B}_{2} & =\frac{36 \pi \times 10^{-7}}{125} T=0.9 \times 10^{-7} T \end{aligned} \] & \[\begin{aligned} \mathrm{B}_{n e t} & =\mathrm{B}_{1}-\mathrm{B}_{2} \\ & =6.28 \times 10^{-7}-0.9 \times 10^{-7} \end{aligned} \] \[\mathrm{B}_{n e t}=5.38 \times 10^{-7} T \] & \[\begin{aligned} \mathrm{B}_{1} & =\frac{\mu_{0} I}{2 r} \\ \mathrm{B}_{1} & =\frac{4 \pi \times 10^{-7} \times 3}{2 \times 3}=2 \pi \times 10^{-7} \mathrm{~T}=6.28 \times 10^{-7} \mathrm{~T} \\ \mathrm{B}_{2} & =\frac{\mu_{0} I R^{2}}{2\left(R^{2}+x^{2}\right)^{3 / 2}} \\ & =\frac{2 \pi \times 10^{-7} \times 2 \times 9}{\left(3^{2}+4^{2}\right)^{3 / 2}} \quad, \text { opposite to } \mathrm{B}_{1} \\ \mathrm{B}_{2} & =\frac{36 \pi \times 10^{-7}}{125} T=0.9 \times 10^{-7} \mathrm{~T} \end{aligned} \] \[\begin{aligned} \mathrm{B}_{n e t} & =\mathrm{B}_{1}-\mathrm{B}_{2} \\ & =6.28 \times 10^{-7}-0.9 \times 10^{-7} \\ \mathrm{B}_{n e t} & =5.38 \times 10^{-7} \mathrm{~T} \end{aligned} \]