Question

Two concentric coils of 20 turns each are situated in the same plane. Their radii are 60 cm and 80 cm and they carry currents 0.4 A and 0.5 A respectively in opposite directions. Calculate the magnetic field at the center.

(a) \(\frac {5\mu_0}{4}\)

(b) \(\frac {5\mu_0}{6}\)

(c) \(\frac {5\mu_0}{8}\)

(d) \(\frac {5\mu_0}{10}\)

The question was asked in my homework.

The query is from Solenoid and Toroid topic in portion Moving Charges and Magnetism of Physics – Class 12

Answer 1

Right choice is (b) \(\frac {5\mu_0}{6}\)

Easiest explanation: Since the two coils are concentric and in the same plane, carrying currents in opposite directions, the total magnetic field at the center of the concentric coils is given by:

B = B1 – B2 = \(\frac {\mu_0}{4\pi } [ \frac {2\pi N_1 I_1}{r_1} ] \, – \, \frac {\mu_0}{4 \pi } [ \frac {2 \pi N_2 I_2}{r_2} ]\)

B = \(\frac {\mu_0}{2} [ \frac {N_1 I_1}{r_1} \, – \, \frac {N_2 I_2}{r_2} ]\)

B = \(\frac {\mu_0}{2} \big [ \)20 × \( \frac {0.4}{0.6} \) – 20 × \( \frac {0.5}{0.8} \big ] \)

B = \(\frac {\mu_0}{2} [ \frac {40}{3} \, – \, \frac {25}{2} ]\)

B = \(\frac {\mu_0}{2} [ \frac {80-75}{6} ] \)

B = \(\frac {5\mu_0}{6}\)