Motional EMF

MOTIONAL EMF

Induced emf due to motion of a conductor in magnetic field

Suppose a conductor is moving with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$. We take a small element PQ = d$\ell$ of the conductor, then induced e.m.f. in the element.

$e=(\vec{v}\times \vec{B}).d\vec{\ell }=V_Q-V_P$

or, e = (vB sin$\theta$). d$\ell$ cos$\alpha$

Where q is the angle between $\vec{v}$

and $\vec{B}$ and$\alpha$is the angle between element and direction of force

Illustration : A metal rod 1.5 m long rotates about its one end in a vertical plane at right angles to the magnetic meridian. If the frequency of rotation is 20 rev/s. Find the emf induced between the ends of rod.

B_H = 0.32 × 10^-4T: Horizontal component of earth's magnetic field.

Solution: Length of rod = 1.5 mt.

Frequency of rotation = 20 rev/sec.

B_H = 0.32 x 10^-4 T

Angular velocity of rod = 20 x 2$\pi$ rad/sec.

emf induced = $B\frac{dA}{dt}$= 0.32 x 10^-4 x 20 x $\pi$x (1.5)²

= 4.5 x 10^-3 V