Home › MHT-CET › Physics › Electromagnetic Induction › A toroid has major radius $R$ and small circular…
A toroid has major radius $R$ and small circular cross-section of radius $r$ ($r \ll R$), with $N$ turns. Its self-inductance is approximately:
A$\dfrac{\mu_0 N r}{R}$
B$\dfrac{\mu_0 N^2 R}{r^2}$
C$\dfrac{\mu_0 N^2 r^2}{2R}$
D$2\pi \mu_0 N R$
Answer & Solution
Correct answer: C. $\dfrac{\mu_0 N^2 r^2}{2R}$
Toroidal magnetic field $B = \mu_0 N i / (2\pi R)$; flux per turn $\phi = B \cdot \pi r^2 = \mu_0 N i r^2/(2R)$. $L = N\phi/i = \mu_0 N^2 r^2/(2R)$ (worked Example 12.5 in textbook).
Related questions
When a rod moves perpendicular to a magnetic field at constant velocity, the FREE charges An LC circuit oscillates with angular frequency ω equal to:Maxwell's correction to Ampère's law introduced:A bar magnet is dropped through a vertical conducting ring. The magnet:A coil of inductance 0.5 H carries a current changing at 4 A s⁻¹. The induced EMF is:A magnetic flux through a coil changes from 4 Wb to 1 Wb in 0.3 s. The average EMF inducedEddy currents are reduced in transformer cores by:A transformer works on the principle of: