Relation Between Magnetism And Electricity

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Relation Between Magnetism And Electricity

It is well known that whenever an electric current flows through a conductor, a magnetic field is

immediately brought into existence in the space surrounding the conductor. It can be said that when

electrons are in motion, they produce a magnetic field. The converse of this is also true i.e. when a

magnetic field embracing a conductor moves relative to the conductor, it produces a flow of electrons

in the conductor. This phenomenon whereby an e.m.f. and hence current (i.e. flow of electrons) is

induced in any conductor which is cut across or is cut by a magnetic flux is known as electromagnetic

induction. 

The historical background of this phenomenon is this :

After the discovery (by Oersted) that electric current produces a magnetic field, scientists began

to search for the converse phenomenon from about 1821 onwards. The problem they put to them￾selves was how to ‘convert’ magnetism into electricity. It is recorded that Michael Faraday* was in

the habit of walking about with magnets in his pockets so as to constantly remind him of the problem.

After nine years of continuous research and experimentation, he succeeded in producing electricity

by ‘converting magnetism’. In 1831, he formulated basic laws underlying the phenomenon of elec￾tromagnetic induction (known after his name), upon which is based the operation of most of the

commercial apparatus like motors, generators and transformers etc.

Force on a Current-carrying Conductor Lying in a Magnetic Field & Fleming left hand rule

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Electromagnetism

Force on a Current-carrying Conductor Lying in a Magnetic Field

It is found that whenever a current-carrying conductor is placed in magnetic field, it experiences a

 force which acts in a direction perpendicular both to the direction of the current and the field. In Fig

. is shown a conductor XY lying at right angles to the uniform horizontal field of flux density B Wb

/m2

 produced by two solenoids A and B. If l is the length of the conductor lying within this field and

 I ampere  the

current carried by it, then the magnitude of the force experienced by it is

the BIl = µ0 µr HIl newton

Using vector notation

F

= I l B

F = IlB sin θ where θ is the angle between l

which

is 90º in the present case

or F = Il B sin 90º = Il B newtons (∵ sin 90º = 1)

The direction of this force may be easily found by Fleming’s left-hand rule.

Hold out your left hand with forefinger, second finger and thumb at right angles to one another.
If the forefinger represents the direction of the field and

the second finger that of the current, then thumb gives the direction

 of the motion. It is illustrated in Fig.

shows another method of finding the direction of force acting on a current carrying conductor. It is
known as Flat Left Hand rule. The force acts in the direction of the thumb obviously, the direction of motor of the

conductor is the same as that of the force. It

 should be noted that no force is exerted on a con￾ductor when it lies parallel to the magnetic field. In general, if the conductor lies at an angle θ with the direction

of the field, then B can be resolved into two components,
B cos θ parallel to and B sin θ perpendicular to the con￾ductor. The former produces no effect whereas the latter is
responsible for the motion observed. In that case,

Fleming left hand rule

F = BIl sin θ newton, which has been expressed as
cross product of vector above.

Absolute & Relative Permiability & Flux Density

Absolute Permeability (μ) and Relative Permeability (μr) 

Magnetic lines

 a bar of a magnetic material, say, iron placed in a uniform field of strength H N/Wb. Suppose, a flux density of B Wb/m2

 is developed in the rod.

Then, the absolute permeability of the material of the rod is defined as
μ = B/H henry/metre 
or 
B = μH 
    = µ0 µr H Wb/m2 ...(i)
When H is established in air (or vacuum), then corresponding flux density developed in air is

B0 = µ0 H

Now, when iron rod is placed in the field, it gets magnetised by induction. If induced pole strength in the rod is m Wb, then a flux of m Wb emanates from its N-pole, re-enters its S-pole and continues from S to N-pole within the magnet. If A is the face or pole area of the magentised iron bar, the induction flux density in the rod is


Bi = m/A Wb/m2

Hence, total flux density in the iron rod consists of two parts 

(i) B0 –flux density in air even when rod is not present
(ii) Bi–induction flux density in the rod


B = B0 + Bi
 = µ0 H + m/A


Eq. (i) above may be written as 
B = µr . µ0 H 
    = µr B0

µr =B/B0

Hence, relative permeability of a material is equal to the ratio of the flux density produced in that material to the flux density produced in vacuum by the same magnetising force.

Flux Density (B) 

 It is given by the flux passing per unit area through a plane at right angles to the flux. It is usually designated by the capital letter B and is measured in weber/meter2 . It is a Vector Quantity. It ΦWb is the total magnetic flux passing normally through an area of A m^ 2
, then
B = Φ/A      Wb/m^2  or tesla (T)

Intensity of Magnetisation (I)

It may be defined as the induced pole strength developed per unit area of the bar. Also, it is the magnetic moment developed per unit volume of the bar.

Let


 m = pole strength induced in the bar in Wb
A = face or pole area of the bar in m^2

Then
 I = m/A    Wb/m^2
Hence, it is seen that intensity of magnetisation of a substance may be defined as the flux density
produced in it due to its own induced magnetism.

If l is the magnetic length of the bar, then the product (m × l) is known as its magnetic moment M.

I= m/A
  = m×l / A×l
  = m/V
  = Magnetic Moment / Volume

Laws of Magnetic Force & Magnetic Field Strength & Magnetic Potential

Here we are going to discuss about magnitism

Magnet

Laws of magnetic Force :

Coulomb was the first to determine experimentally the quantitative expression for the magnetic force between two isolated point poles. It may be noted here that, in view of the fact that magnetic poles always exist in pairs, it is impossible, in practice, to get an isolated pole. The concept of an isolated pole is purely theoretical. However, poles of a thin but long magnet may be assumed to be point poles for all practical purposes  By using a torsion balance, he found that the force between two magnetic poles placed in a medium is


(i) directly proportional to their pole strengths

(ii) inversely proportional to the square of the distance between them and


(iii) inversely proportional to the absolute permeability of the surrounding medium.

Magnetic Field Strength (H)

Magnetic lines

Magnetic lines of force

Magnetic field strength at any point within a magnetic field is numerically equally to the force experienced by a N-pole of one weber placed at that point. Hence, unit of H is N/Wb. Suppose, it is required to find the field intensity at a point A distant r metres from a pole of m webers. Imagine a similar pole of one weber placed at point A. The force experienced by this pole is

Magnetic Potential :

The magnetic potential at any point within a mag￾netic field is measured by the work done in shifting a N-pole of one weber from infinity to that point against the force of the magnetic field. It is given by