# What is the Average Induced EMF in a Rotating Coil?

• jemerlia
In summary, a rectangular coil of 200 turns with dimensions 200 mm x 120 mm rotates at a constant angular speed of 40pi rad/s in a magnetic field of 2.4 x 10-2 T. The maximum induced electromotive force is 14.47V when the coil's plane is parallel to the magnetic field, and it decreases to 14.29V when the coil rotates through an angle of 1/(2pi) radians. However, the given result is 9.216V, indicating a potential error in the calculations. Further help and advice is requested from anyone reading this conversation.
jemerlia

## Homework Statement

A rectangular coil of 200 turns has a length of 200 mm and width
120 mm. The coil rotates with a constant angular speed of 1200
revolutions per minute about an axis through the midpoints of its
longer sides in a uniform magnetic field of 2.4 x 10-2 T.

Starting from a time when the coil’s plane is parallel to the
magnetic field, calculate the average induced electromotive
force whilst the coil is turning 1/(2pi) radians.

## Homework Equations

E(emf) = N x B x w x A x sin (theta)
where N = number of turns
B = magnetic field (T)
A = area of coil
theta = angle made by coil wrt perpendicular to the field

## The Attempt at a Solution

Angular velocity = 40pi (1200rpm)

As the coil rotates through the field plane the induced emf is at the maximum (sin (theta) = 1)
where
E = 200 x 2.4 x 10-2 T x 40pi x 0.120m x 0.200m x sin (pi/2) = 14.47V

After rotating towards the vertical through the rather small angle 1/(2pi) radians:
E = 200 x 2.4 x 10-2T x 40pi x .120m x .200m x sin (pi/2 - (1/(2pi)) = 14.29V

The given result is 9.216V so I've obviously missed something. Yet - it seems unusual that after rotating through such a small angle that the induced voltage should fall as low as the given answer.

if w=1200rpm why do you have 1200*40pi?

I am not using 40pi * 1200: the rotational speed is 40pi which is used in the expression which requires angular velocity in rad/s. The 40pi comes from converting 1200rpm to rad/s. I then use the value 40pi for w (omega) in the expression..l.

## 1. What is "Emf induced in rotating coil"?

Emf induced in rotating coil refers to the process of generating an electromotive force (or voltage) in a coil of wire that is rotating in a magnetic field. This phenomenon is also known as electromagnetic induction and is the basis for the operation of generators and motors.

## 2. How does a rotating coil produce an Emf?

When a coil of wire is rotated in a magnetic field, the magnetic field lines cut across the wire and induce a voltage in the wire. This voltage is caused by the changing magnetic flux through the coil, and is proportional to the rate of change of the magnetic field and the number of turns in the coil.

## 3. What factors affect the magnitude of the Emf induced in a rotating coil?

The magnitude of the Emf induced in a rotating coil depends on the strength of the magnetic field, the speed of rotation, the number of turns in the coil, and the angle between the coil and the magnetic field. Additionally, the shape and size of the coil and the type of material used can also affect the induced Emf.

## 4. How is the direction of the induced Emf determined in a rotating coil?

The direction of the induced Emf in a rotating coil is determined by the right-hand rule. If you point your right thumb in the direction of the magnetic field, and your fingers in the direction of rotation, then the direction of the induced Emf will be perpendicular to both your thumb and fingers.

## 5. What are the practical applications of Emf induced in rotating coils?

The Emf induced in rotating coils is used in a variety of applications, including generators, motors, and transformers. It is also used in devices such as electric meters, induction heaters, and induction cooktops. It is an essential principle in the field of electromagnetism and has numerous technological and industrial applications.

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