Two concentric coils of radius \( 2\pi \) cm each are placed with their planes at right angles to each other and carry currents of 3 A and 4 A, respectively. The net magnetic field in \( \mathrm{Wb/m^{2}} \) at the center of the coils will be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 5\times10^{-5} \)
Each coil produces a field \( B = \mu_0 I/2R \) at the centre, along the axis of that coil. The planes are at right angles, so the two fields are perpendicular and add as vectors.
\( \displaystyle R = 2\pi\,\mathrm{cm} = 2\pi\times10^{-2}\,\mathrm{m} \)
\( \displaystyle B = \frac{\mu_0 I}{2R} = \frac{4\pi\times10^{-7}\,I}{4\pi\times10^{-2}} = 10^{-5}\,I \)
\( B_1 = 10^{-5}\times3 = 3\times10^{-5}\,\mathrm{T} \)
\( B_2 = 10^{-5}\times4 = 4\times10^{-5}\,\mathrm{T} \)
\( \displaystyle B_{\mathrm{net}} = \sqrt{B_1^{2} + B_2^{2}} = \sqrt{9 + 16}\times10^{-5} = 5\times10^{-5}\,\mathrm{T} \)