Question

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

Answer 1

Here $r_1=5cm,r_2=10cm$

$n_1=50,n_2=100$

Current $i_1=i_2=5A$

(a) $B=\frac{{\mu }_0{n}_1{i}_1}{2r_1}+\frac{{\mu }_0{n}_2{i}_2}{2r_2}$

$=\frac{4\pi \times {10}^{-7}\times 50\times 5}{2\times 5\times {10}^{-2}}+\frac{4\pi \times {10}^{-7}\times 100\times 5}{2\times 10\times {10}^{-6}}$

$=4\pi \times 250\times {10}^{-6}+4\pi \times 250\times {10}^{-6}$

$=2\times 4\pi \times 250\times {10}^{-6}T$

$=2\pi \times {10}^{-3}T.$

(b) Clearly, when currents are in opposite direction.

B at centre = 0.