MAGNETIC EFFECT OF CURRENT
BIOT SAVART'S LAW :-
The magnetic field (in magnitude) at a point at a diastance r frm a current carrying element of length dl n carrying a current I is given by
db = 
o/4
. I [dl * r]/r3 = o/4. I dl sin
/r2
where is the angle b/w the direction of the current n the line joining the current elements to the observation point n o is absolute permeability of the free space.
The direction of the magnetic field dB is tht of I dl * r .It can also b found by right hand thumb rule.
MAGNETIC FIELD DUE TO A CURRENT CARRYING CONDUCTOR :-
The magnetic field at a point at perpendicular diastance r frm a straight conductor carrying current I is given by
B = o/4. I/r(sin
1 + sin2)
where 1 n 2 r angles which the lines joining the two ends of the conductor to the observation point make with the perpendicular frm the observation point to the conductor.
In case the straight conductor is of infinite length (1= 2 = /2) the magnetic field is given by
B = o/4. 2I/r
MAGNETIC FIELD DUE TO A CURRENT CARRYIING CIRCULAR COIL :-
For a coil of radius r , consisting of N turns n carrying a current I
a) The magnetic field at a point on the axis at a distance x frm its centre is
B = o/4 . 2 N I r2 /(r2 + x2)3/2
b) The magnetic field at its centre :-
AMPERE'S CIRCUITAL LAW :-
The line integral of magnetic field B around any closed path or a circuit is equal to o times the total current I threading through the circuit
B.dl = oI
MAGNETIC FIELD DUE TO A SOLENOID :-
If a solenoid of N turns per unot length carries a current I, then
a) magnetic field at a point well inside the solenoid is
B = oN I
b) magnetic field at a point on one end of the solenoid is
B = 1/2 oN I
Note :-
1. Whereas the source of electric field is an electric charge, the source of
magnetic field is a current element( not a magnetic charge)
2. The magnetic field due to a straight conductor is zero, when the observation
point lies along the length of the conductor.
3. The magnetic field due to a part of a circular conductor of radius r n carrying
current I is
where is the angle which the circular part subtends at its centre.
4. When a current I flows through two concentric conductor of radius a1,n a2
net magnetic field at their centre is
B = o/4 . 2 I (1/a1 + 1/a2)
when current flows in same direction n by the relation
B = o/4 . 2 I (1/a1 - 1/a2)
when current flows in opposite direction through the two circular conductors
5. For a point on the axis of a circular coil carrying current, magnetic field is
max. at the centre of the coil.
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