Demonstrative Video
Production of Torque
The torque produced by the alignment of two fields (i.e., rotor field and stationary main field) varies in magnitude and direction depending upon the torque angle \(\theta\).
Let us see, the effect of torque angle \(\theta\) on the torque produced in the following cases:
In case of permanent magnet
In case of electromagnet
In Case of Permanent Magnet
\[\begin{aligned}
\theta &=\text { angle between the axis of two fields }
F_{m} \text { and } F_{r^{\prime}} \\
l &=\text { length of magnet } A . \\
r &=\text { radius of circle in which rotation takes place.
} \\
F &=\text { force acting on north and south pole of magnet }
A . \\
\text { Torque } &=\text { Force } \times \text {
Perpendicular distance. }
\end{aligned}\]
\[\begin{aligned} \text{In a right angled triangle 'oab'} ~ab&=oa\sin\theta \\ \text{Distance perpendicular to force}, ab &= r \sin \theta \end{aligned}\] \[\begin{aligned} \text{Torque} & = 2F \times r\sin\theta = 2F \times \dfrac{l}{2}\sin\theta \\ T & = Fl\sin\theta ~[F=\dfrac{m_1m_2}{4\pi\mu_0\mu_rd^2}] \\ T & = K\sin\theta ~~[\text{where}~K=F\times l~\text{is constant}]\\ T &\propto \sin \theta ~~[\text{maximum}~\theta=90^{\circ}] \end{aligned}\]
In Case of Electromagnet
\[\begin{aligned}
F &=\text { Force acting on the two conductors. } \\
r &=\text { radius of circle in which conductor rotates. }
\\
\theta &=\text { angle between the field } F_{m} \text { and
} F_{r^{\prime}}
\end{aligned}\]
In a right angle triangle, angle \(a o b=\theta\)
Distance perpendicular to force, \(a b=o a \sin \theta =r \sin \theta\)
Total torque acting on the two conductors, \(T=2 F_{r} \sin \theta\)
where \[\begin{aligned} B&= \text{Flux density of the main field}\\ I&= \text{Current flowing through the conductor}\\ l &= \text{Effective length of conductor} \end{aligned}\]
\[\begin{aligned} T&=2 B I l r \sin \theta\\ T&=K_{L} \sin \theta \quad\left[\text { Where, } K_{l}=2 B I l r \text { is a constant }\right]\\ T &\propto \sin \theta \end{aligned}\]
Production of Unidirectional Torque
Alignment of two fields torque develops but the torque produced is not unidirectional.
The unidirectional or continuous torque can be obtained by applying any one of the following methods.
By Rotating the Main Magnets they drag the other magnets free to rotate (or the armature, electromagnet) along with it because of the tendency of the field of free rotating magnet or armature to align with the field of main magnet
By Changing the Direction of Flow of Current in the Conductors of Electromagnet (armature) in such a manner that the conductors facing a particular main field pole, always have the same direction of flow of current.