THE MAGNETIC FIELD: -
“The region around a source magnet where its effect can be felt on a test magnet is called magnetic field”
It is vector field and is represented by lines which are called magnetic lines of forces and magnetic lines are the direction on which the North Pole test magnet move when place in the filed of source magnet. Unlike electric field line magnetic field lines are closed in nature. The magnetic field is specified at each of its point by a vector B called the magnetic induction or magnetic flux density.
MAGNETIC FIELD DUE TO CURRENT IN STRAIGHT WIRE: - Oersted is a great scientist who first time showed that, when current is passed through a straight wire, it deflects a near by compass needle. Thus a current carrying wire produce magnetic field around itself. The direction of this magnetic field can be found by right hand rule.
RIGHT HAND RULE: - “If the wire is grasped in right hand with the thumb pointing in the direction of the conventional current, the fingers of the hand will circle the wire in the direction of magnetic field”
The generalization of Oersted observations leads us to the concept of electromagnet. i.e. a current carrying coil act like a magnet which is known as electromagnet.
FORCE ON CURRENT CARRYING CONDUCTOR IN MAGNETIC FIELD: -
If we place a conductor of length L carrying current I in uniform magnetic field of magnetic induction B, it (the conductor) experiences a force of reaction. It can be easily understand by the following experiments.
EXPERIMENTS: - Let’s suppose that the magnitude of this force is directly proportional to the current “I”, magnetic induction “B” and component of “L” perpendicular to B. i.e.
F ∞ IL × B F = K I L × B
F = K I L B Sin Ѳ
Where K is proportionality constant and its value is 1 so therefore the above equation can also be written as
F = I L B Sin Ѳ (1)
If the wire is perpendicular to the field then Ѳ = 900 then the forced is maximum so therefore the above equation is
FMax = I L B [ I ^ B ]
Similarly if the wire is parallel to the field then Ѳ = 0 then the force is zero.
UNIT: - In international system the unit of magnetic field is TESLA and tesla is defined as,
“One Newton force is applied on one meter length of the conductor which is placed there at right angles to the field when a current 1A passes through the conductor”.
In cgs system the unit of magnetic field is GAUSS (G) and 1 G = 10 – 4 T or 1 T = 104 G
MAGNETIC FLUX: -
“The number of magnetic field lines (lines of induction) passing through an area element gives the magnetic flux through that element”.
Mathematically it is the scalar product of magnetic induction (B) and vector area ∆A. i.e.
∆φ = B • ∆A = B∆ACosѲ (1)
Where Ѳ is the angle between B and ∆A and ∆φ is representing the magnetic flux through area element. The net flux through area A can be obtained by calculating the flux through each area element and then summing up all the fluxes. i.e.
φ = ∆ φ1 + ∆ φ2 + ∆ φ3+ . . . . . . . . + ∆ φn
= B1 • ∆A1 + B2 • ∆A2 + . . . . . . . + Bn • ∆An (2)
If the field is uniform and the area is plane then equation (2) becomes
φ = Bi • ∆Ai = B ∆ Ai CosѲ
φ = B CosѲ (∆ Ai )
φ = B Cos Ѳ {A} = BA Cos Ѳ (3)
This equation gives the flux through plane area when placed in uniform magnetic field, and it shows that flux is maximum if Ѳ = 00. i.e.
φmax = BA Cos 00 = BA (1) = BA
Similarly equation (3) gives the flux is zero when Ѳ = 900 because Cos 900 = 0
UNIT: - It is a scalar quantity and its unit is WEBER and Weber is defined as, “the flux passing through 1m2 area placed at right angle to B in a region where the magnetic induction is one tesla is called one Weber”. i.e. 1Wb = 1m2 T
FLUX DENSITY: - Flux density is another name for magnetic induction and can be defined as,
“The flux per unit area”
The flux passing through an area element ∆A placed at right angle to B is given by
∆φ = B∆A Cos00 = B∆A
B = (∆φ / ∆A)
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