# Periodic EMI

Suppose a rectangular coil having

*N*turns placed initially in a magnetic field such that magnetic field is perpendicular to its plane as shown in Fig. 11.For uniform rotational motion with

*Ï‰*, the flux linked with coil at any time*t**Ï†*=

*NBA*cos

*Î¸*=

*NBA*cos

*Ï‰t*

where

*Ï†*_{0}=*NBA*= maximum flux*Ï‰*â€“ Angular speed

*v*â€“ Frequency of rotation of coil

*R*â€“ Resistance of coil

**Fig. 11**

# Induced emf in coil

Induced emf also changes in periodic manner. That is why this phenomenon called periodic EMI

â‡’

*e*=*e*_{0}sin*Ï‰t*where

*e*_{0}= emf amplitude or maximum emf =*NBA**Ï‰*=*Ï†*_{0}*Ï‰*# Induced current

At any time

*t*,where

*i*_{0}= current amplitude or maximum current

*Notes:*- In motional emf are three vectors. If any two vectors are parallel, no flux cutting.

**Fig. 12**

- A piece of metal and a piece of non-metal are dropped from the same height near the surface of the earth. The non-metallic piece will reach the ground first because there will be no induced current in it.
- If an aeroplane is landing down or taking off and its wings are in the eastâ€“west direction, then the potential difference or emf will be induced across the wings. If an aeroplane is landing down or taking off and its wings are in the northâ€“south direction, then no potential difference or emf will be induced.
- When a conducting rod moving horizontally on equator of earth no emf induces because there is no vertical component of earthâ€™s magnetic field. But at poles
*B*is maximum so maximum flux cutting. Hence, emf induces._{V}