This document discusses the torque acting on a coil placed in a rotating magnetic field. It explains that an emf is induced in the coil due to the rotating magnetic field. According to Lenz's law, the coil will rotate in the direction of the rotating field to minimize the relative velocity. This causes a torque on the coil tending to rotate it in the direction of the magnetic field. The document then provides equations to calculate the induced emf, current, magnetic moment, and torque experienced by the coil in the rotating magnetic field. It determines that the maximum torque occurs when the frequency of rotation ω is equal to the resistance R over the self-inductance L of the coil.

1. Torque Acting on a coil placed in
a rotating magnetic field
I PHYSICS – 06.04.2022
Dr.R.Hepzi Pramila Devamani,
Assistant Professor of Physics,
V.V.Vanniaperumal College for Women,
Virudhunagar.

2. Torque Acting on a coil placed in a rotating
magnetic field
• If a coil is placed at the centre O of the rotating magnetic field,
an emf is induced in it due to the rotating magnetic field.
• The conductor begins to rotate in the direction of rotating
magnetic filed so that the relative velocity between the
conductor and the rotating magnetic field becomes least
according to Lenz’s law.
• Thus a torque acting on a coil , tending to rotate in the
direction of the resultant field.
• Let us calculate the torque experienced by the coil when
placed in a rotating magnetic field.

3. Torque Acting on a coil placed
in a rotating magnetic field
• Let a coil CC of N turns and area A be placed in a rotating
magnetic field of flux density B with its centre at O.
• The total magnetic flux φ linked with the coil at any instant t is
• Φ = NAB sin ωt
• Here ωt is the angle between B and the plane of the coil.
• Hence the induced emf in the coil is
• Ε = - dΦ / dt = - d(NAB sin ωt)/dt
• = - NBAω cos(ωt-π)
• Let r be the resistance and
• L the self Inductance of the coil

4. Torque Acting on a coil placed
in a rotating magnetic field
• The induced current in the coil is
• Where tan α = ω L/R.
• The current lags behind the emf by an angle α.
• The current gives rise to a magnetic field and the coil
behaves as a magnetic shell of magnetic moment N/Ai.
• The magnetic moment is directed along the normal to the
coil in the direction OM.

5. Torque Acting on a coil placed
in a rotating magnetic field
• The torque acting on the coil tending to turn it in the
direction of B is

6. Torque Acting on a coil placed
in a rotating magnetic field
• The average value of cos2ωt over one cycle is ½ and
that of sin ωt cos ωt is zero. Therefore, the mean
torque acting on the coil is

7. Torque Acting on a coil placed
in a rotating magnetic field
• The variation of τ̅ with ω is shown in fig.
• This torque acts in the direction of the rotating
magnetic field. As a result, the coil rotates
continuously.
• The torque is zero if ω = 0 or ∞. Therefore for a
certain value of ω lying in between
0 and ∞ the torque must be a
maximum.

8. Torque Acting on a coil placed
in a rotating magnetic field
• Differentiating eq.(2) w.r.t. ω and equating the result
to zero. We have,

9. Torque Acting on a coil placed
in a rotating magnetic field
• Hence τmean is maximum for ω = R/L
• Again tan α = ωL/R = 1 or α = 450
• Thus the value of α for maximum torque is 450
• The value of maximum torque is obtained by putting
ω = R/L in eq.(2)
• Induction motors are constructed both for single
phase and three phase operation

10. THANK YOU