Basics of ELECTROMAGNETISM

What is Electromagnetism?

Electromagnetism, the study about electromagnetic force is a branch of Physics which is the most important in Electrical Engineering.

Electrical Machines are build upon the principle of Electromagnetism, to transfer the electrical energy or to convert the energy from one form to another.

Electromagnetism means electrical field and magnetic field are interrelated. That means Electromagnetism has two part-i. Electrical field and ii.Magnetic field.

• A time varying electrical field(dE/dt) can lead to induction of magnetic flux density(B) or magnetic field(H)
• Similarly a time varying magnetic field can lead to an induced Electric field(E).

                          ---It is Electromagnetism that means Electricity can be converted to magnetism or magnetism can be converted to electricity.

Such some laws which is related to electrical domain and magnetic domain, called Laws of Electromagnetism.

What is Electromagnetic Force ?

>> It's a force that acts between charged particles and is a combination of electrical and magnetic forces.

Suppose a charge '±q' is moving in a magnetic field with  velocity 'V', then the charge experiences a force, called electromagnetic force.

                                ∴ Electromagnetic force,  F=±q(𝐕x𝐁)  where 𝐁=Magnetic flux density

 N.B. - 'q' must have sign.

• Faraday's Law : -

  Whenever there is time varying magnetic flux, then electromotive force(emf) is induced in the conductor or in the circuit which is proportional to rate of change of the flux linkage.

                                              ∴ EMF (E) =  d⋋/dt                        ⋋ = Flux linkage

    what is the difference between flux(∅) and flux linkage(⋋)?

  
 >>   Suppose we take a coil of 'N' number of turns and placed it in a magnetic field. Due to magnetic field there will be flux. The total flux may or may not be cut the coil . So how much of total flux is linking with the coil is called flux linkage(⋋).

   

                                                

   ∴ ⋋=N∅     where ∅=Total flux  

Basic Requirements to satisfy Faraday's Law :-

i. Magnetic field (because need of flux)
ii. Set of Conductors ( so that emf can induced in the set of conductors)

      N.B.- The set of conductors can be in the form of coil or in the form of simple conductors.

iii. Relative Variation - ( There must be relative variation between set of conductors and magnetic field , then only emf can induced as per faraday's rule.)

What is Relative Variation?

>> One quantity among the set of conductors and magnetic field , may be set of conductors or magnetic field is varied with the varying of time. There are two types of variation - i. Relative Time 

variation and ii. Relative Space Variation.

• Relative Time Variation :  Magnetic flux density is varying with time that means Magnetic                                                     flux density(B) is a function of time.

                                                                      ∴B→B(t)

                                                                 As, Φ =B(t)*A             where A=  Cross sectional Area

                                                                      ∴ Φ→Φ(t)

                                            that means flux is also varying with time.

                                                              then, EMF(E) = dΦ(t)/dt

                                 This type of induced emf is called Statically induced emf. 

So, whenever there is a time varying flux, an emf will be induced in the coil that termed as Statically induced emf. 

But the conductors must be stationary that means the system is stationary. This type of emf is induced in case of Transformer. That means in transformer  the induced emf is static in nature.

• Relative Space Variation :   The position of conductors must be changing with respect to magnetic field.  

This sort of variation results in Dynamically induced emf.  (Example- Generators, Motors)

How does the electromagnetic force leads to induction of an emf in a conductors?

>> Lets consider for two types of induced emf.

• Dynamically Induced EMF :       

Suppose a conductor PQ or a coil PQ is moving with velocity 'V' in  a magnetic field 'B' .
                                  ⛒➝ denotes inside the paper
   if PQ has '+q' charge.

                                  so , force,  F=q(𝐕x𝐁)

So positive charge will experience a force in a particular direction.

To know the direction  that means keep your finger in the direction of 𝐕 and curl them in the direction of 𝐁. Then the direction of thumb shows the direction of magnetic force which is upward. so positive charge will experience a force in the upward direction. Hence the positive charges will start collecting on the top of the conductor.

 if PQ has '-q' charge. then   F=-q(𝐕x𝐁).

Due to -ve sign the direction of force will be downwards. So the negative charges will start collecting in the bottom of the conductor.

So we have a conductor with positive(+) charges at the top and the negative(-) charges at the bottom, that means an electric field will be induced from positive to negative.

As Electric field is downward , the force on positive charge will be downward but the force on negative charge will be upward(opposite to the field).

But the magnetic field is trying to push the negative charge in downwards where as electric field is trying to push upward. So both the forces are opposite. At first there is net force on the negative charge or on the electrons. Electrons will keep moving but as soon as both the forces balance each other, then the net forces on the charge will be zero. The the charge will stop moving.  So we are considering the steady state condition when the charge is not in motion and charge has stop accumulating at the both ends. That means

                                                  q𝐄=q(𝐕x𝐁)         where q𝐄=Force in electric field

                                                   ∴ 𝐄=(𝐕x𝐁)         and q(𝐕x𝐁)= Force in magnetic field

                                                                                            𝐄=induced emf

                ∴ Potential Difference, PD = -∫𝐄.dl
                                                            =-∫(𝐕x𝐁).dl
 As 𝐕 is rightward and 𝐁 is inward that means 𝐕 and𝐁 are perpendicular, 
                                                     then  PD = BLV
This 'PD' is termed as Dynamically Induced Emf. and it's also called as Motional Emf because Emf is induced by virtue of motion of the conductor inside a magnetic field.
This type of Emf is induced in rotating electrical machine.

•  Statically Induced Emf :

Statically Induced Emf means Emf is induced in the stationary conductors. 
Lets take a coil whose flux(Φ) is a function of time.

             ∴ Φ = f(t)
                    =ΦₘCosωt
          As Emf,  EMF (E) =  d⋋/dt   where N=no of turns of Inductor
                        E = -NωΦₘ Sinωt             and ⋋=flux linkage
                         E = -N*dΦ/dt
            This -ve sign represents the Lenz's law.

•          Lenz's Law :-

Induced emf opposes the cause of induction , so that induction does not happen. Thats why we are showing -ve sign ⇒ E = -N*dΦ/dt
Example : In generator Emf(E) is induced due to Prime mover torque (Tₚₘ). Due to induced Emf(E), a current(I) will flow in the circuit. So This produced current(I) will oppose the cause of induction and the cause of Induction is Prime mover torque (Tₚₘ).
Now the question is How it oppose?
→The current(I) causes an additional torque (Tₑₘ) which is electromagnetic torque or induced torque. this induced toque will oppose the prime mover toque.

                                                          ∴ T=Tₚₘ-Tₑₘ

• Self Induced Emf :-

The Emf induced in the coil due to the change of flux produced by linking with its own turns.

Lets take a coil whose flux(Φ) is a function of time.

             ∴ Φ = f(t)
              and ⋋=NΦ
                E = -N*dΦ/dt
This is self induced emf, that means The coil itself is responsible for self induced Emf. 
            Self Inductance,L =Φ/i
             Flux linkage, ⋋=(μ₀N²A)i/l               where N= No of total turns on coil , l=length of the coil
                            ∴  L= (μ₀N²A)/l                               and A= Cross-Sectional Area of the coil.

• Mutually Induced Emf :-     

When flux produced by one coil links to other coil and produces emf in the other coil, it is called Mutually induced Emf. 
 If the no of turns in coil1 is N₁ and in coil2 is N₂ , 
then Induced emf,E = -N₂dΦ(t)/dt
and Mutual Inductance, M = (μ₀N₁N₂A)/l