Electromagnetic Induction Concept Page - 1

Definition

Electromagnetic Induction

The property due to which a changing magnetic field within a closed conducting coil induces electric current in the coil is called electromagnetic induction.

Definition

Flux linkage

For a closely wound coil of N turns, the same magnetic flux is linked with all the turns. When the flux ϕB${\varphi }_B$ through the coil changes, each turn contributes to the induced emf. Therefore, a term called flux linkage is used which is equal to NϕB$N{\varphi }_B$ for a closely wound coil and in such a caseNϕB∝I$N{\varphi }_B\propto I$

Definition

Magnetic flux through an area

Magnetic flux is a measure of the quantity of magnetism, being the total number of magnetic lines of force passing through a specified area in a magnetic field. Magnetic flux through a plane of area A placed in a uniform magnetic field B can be written as 
ϕB=B.A=BAcosθ${\varphi }_B=B.A=BAcos\theta$

Definition

Magnetic flux density

Magnetic Flux Density is amount of magnetic flux through unit area taken perpendicular to direction of magnetic flux. Flux Density (B) is related to Magnetic Field (H) by B=μH. It is measured in Webers per square meter equivalent to Teslas [T].

The total number of magnetic field lines passing through a given area normally is called magnetic flux. In magnetic flux formula μ is the permeability of the medium (material) where we are measuring the fields. The B field is a vector field, which means it has a magnitude and direction at each point in space.

Definition

Factors affecting induced emf

So, emf is dependent on number of turns of coil,shape of the coil, strength of magnet and speed with which magnet is moved. Emf is independent of resistivity of wire of the coil.

Definition

Fleming's right hand rule

Fleming's right hand rule is used to determine the direction of induced current in a coil. If the thumb (direction of motion), index finger (along magnetic field) and middle finger are held mutually perpendicular as shown in the figure, then middle finger gives the direction of induced emf in the wire.

Definition

Generation of electric current due to relative motion

When a bar magnet is moved inside a coil connected to a galvanometer, then the motion induces a deflection in the galvanometer signalling the presence of electric current.Further, the deflection (and hence current)is found to be larger when the magnet is pushed towards or pulled away from the coil faster. Instead,when the bar magnet is held fixed and the coil is moved towards or away from the magnet, the same effects are observed. It shows that it is the relative motion between the magnet and the coil that is responsible for generation (induction) of electric current in the coil.

Definition

Induced EMF

The magnetic flux is a measure of the number of magnetic field lines passing through an area. If a loop of wire with an area A is in a magnetic field B, the magnetic flux is given by:
ϕ=BAcosθ$\varphi =BAcos\theta$ , where θ$\theta$ is angle between magnetic field B and vector area A which is perpendicular to plane of loop.

If the flux changes, an emf will be induced. There are 3 ways an emf can be induced in a loop:

1. Change the magnetic field
2. Change the area of the loop
3. Change the angle between the field and the loop

Example

Induced emf in a closed loop

An annular circular brass disk of inner radius r$r$ and outer radius R$R$ is rotating about an axis passing through its center and perpendicular to its plane with a uniform angular velocity ω$\omega$ in a uniform magnetic field of induction B$B$ normal to the plane of the disk. The induced emf between the inner and the outer edge of the annular disk is:d(emf)=−Bwxdx$d\left(emf\right)=-Bwxdx$
emf=−∫RrBwxdx$emf=-{\int }_r^{R}Bwxdx$
=−Bw[x22]Rr$=-Bw[{\displaystyle \frac{x^2}{2}}{]}_r^R$
=Bw(R2−r22)$=Bw\left({\displaystyle \frac{R^2-r^2}{2}}\right)$
Emf between inner and outer edge will be
=Bw(R2−r22)$=Bw\left({\displaystyle \frac{R^2-r^2}{2}}\right)$

Definition

Faraday's Experiment

A galvanometer is connected to an insulated copper coil.When magnet is moved towards or away fromt he coil, the following things happen:
1. If the magnet and coil is at rest then no deflection is observed in galvanometer G.
2. When the N pole of magnet is moved towards coil, then the galvanometer gives deflection in one direction fig b
3. when magnet is stopped deflection becomes zero
4. When N pole is moved away from the coil, the galvanometer gives deflection in opposite direction.
5. If magnet is moved fast deflection increases
6. If number of turns is increased then deflection also increases.
7. The induced current is produced only by relative motion between magnet and coil.

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