**Electromagnetic Induction**

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The process by which a changing magnetic flux produces electric current is called **electromagnetic induction**. The current and the emf produced are called induced current and induced emf, respectively.

Three physicists worked individually to test whether a magnetic field could produce an electric current. They were:

** Joseph Henry (USA)**

** **** Michael Faraday (UK)**

** **** Heinrich Friedrich Lenz (Russia)**

But Faraday was given the credit for the discovery of electromagnetic induction since he was the first one to publish his findings. *Given the idea, it is the change in magnetic flux that produces electric current*.

**Michael Faraday** began to experiment with magnets and current-carrying wires at the Royal Institutes of London in 1831. His observations included the following:

*(a)* When he thrust a magnet into a coil of wire, current was induced in the coil while the magnet was moving relative to the coil. Moving the magnet away from the coil caused the galvanometer to deflect in the opposite direction.

*(b)* Moving the magnet toward the coil had the same effect as moving the coil toward the magnet; only the relative motion was important.

Faraday’s observations can be summarized in the famous **Faraday’s law** which says that* the emf induced in a loop of wire is proportional to the rate of change of magnetic flux through the coil.*

**Joseph Henry** published the results of his work in 1832. He explained that a changing electric current in a coil can induce another current in the same coil. As a result, the current in the coil consists of two components, the initial current plus an induced current. This effect is known as **inductance**.

**Heinrich Friedrich Lenz** extended our understanding of induction of currents by stating a related law. **Lenz’s Law** states that *the direction of an induced current is such that its own magnetic field opposes the original change in magnetic flux that induced the current.*

Faraday’s and Lenz’s laws are in accord with the law of conservation of energy. When a magnet is moved closer to a coil, or the coil is moved toward the magnet, by Faraday’s law, an emf is created that can generate an electric current if the coil is closed circuit; and Lenz’s law, the direction of this induced current is such that the resulting magnetic fields an opposing force on the moving magnet.

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The work of these three famous physicists made possible the process of electromagnetic induction, or the process of inducing a current by moving a magnetic field through a wire coil. * Figure 1.1 A *shows how electromagnetic induction occurs. As the wire coil moves through a magnetic field, it induces an electric current.

*(Voltage is always induced. Current is induced only if the circuit is closed.)*The direction of the wire coil’s motion affects the direction of the electric current.

These are some important concepts to understand electromagnetic induction:

** It occurs any time motion takes place between the wire and the magnetic field.**

** The results are the same when the wire moves, when the magnetic field moves, or when both move.**

** The speed of the motion affects the strength of the electric current; that is, a weak current is produced when the movement of the wire or the magnetic field is slow and a strong current is produced when the movement is fast.**

** The number of loops in the wire affects the strength of the voltage; that is, a larger number of loops means a stronger voltage (Figure 1.1 B)**

** Any changing magnetic field will induce a current.**

Combining Faraday’s Law and Lenz Law, we have

**E = -N ∆**ɸ**/∆t**

where E is the induced emf, N is the number of turns, ∆ɸ is the change in flux and is equal to ∆t is the time elapsed. The magnetic sign means that the induced emf sends current in a direction so as to oppose the change in flux causing it.

**General Definition of Magnetic Flux**

What is magnetic flux? What constitutes a change in magnetic flux?

**Magnetic flux** is defined as the product of the area of the surface swept out by the moving conductor and component of the magnetic field B that is perpendicular to this area. In symbols

ɸ** = BAcos**ɸ

where B is the magnetic field strength, A is the area and ɸ is the angle between the magnetic field and a line perpendicular to the area. Faraday’s law states that an induced current is produced whenever the flux changes. The flux depends on the magnetic field B, area A and the angle ɸ. A change in any of these factors constitutes a change in flux.

**Sample Problem 1.1**

A coil of wire is situated in a o.5 T uniform magnetic field. The area of the coil is 2.o m^{2}. What is the magnetic flux if the angle between the magnetic field and the normal to the surface of the coil is 60 degrees? After 5 sec, the magnetic field is now parallel to the normal to the surface. What is the induced emf?

**Given: ** B = 0.5 T

ɸ= 60 degrees

A = 2.0 m^{2}

**Using the equation: **ɸ = BAcosɸ

ɸ= (0.5T)(2m^{2})cos60˚

ɸ= 0.5 Wb

**After 5s, the flux is: **ɸ= (0.5T)(2m^{2})cos0˚

ɸ= 1 Wb

**Solving for the induced emf: **E = -N ∆ɸ/∆t

E = (-1 Wb x 0.5 Wb)/ 5 s

E = -0.1 V

**Induced EMF in a Moving Conductor**

It was shown earlier that when a conducting wire is moved through a magnetic field, current and, hence emf are induced in the wire. The emf generated when a wire of length L is moved with a velocity v that is perpendicular to a magnetic field B is called **motional emf** and is given by

**E = -vBL**

Again, the negative sign is in accordance with Lenz law.

The generator rule gives the direction of the induced current in a wire moving at right angles to a magnetic field.

*“If the thumb, forefinger, and middle finger are held at right angles to each other, the forefinger points in the direction of the magnetic field, the thumb in the direction of the motion, and the middle finger in the direction of the induced current.”*

**Sample Problem 1.3**

A wire 1.0 m long moves with a speed of 50 m/s through a uniform field of strength 0.5 T if the wire, magnetic field, and motion are mutually perpendicular, what is the emf produced?

**Given:** B= 0.50 T

v=50 m/s

L=1.0 m

**Find:** motional emf

**Equation:** E=-vBL

**Solution: ** E=-vBL

E=-(50 m/s)(1.0 m)(50 m/s)

E=-25 v

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