## Magnetic Field

Magnetic Field- 1) It is a region or space around a magnet or current carrying conductor or a moving charge, in which its magnetic effect can be felt.
2) The conductor carrying current is electrically natural but a magnetic field is associated with it.
3) The strength of magnetic field at a point is represented by the vector B, Which is called magnetic field induction or magnetic flux density vector.
4) Magnetic field induction is a vector quantity.
5) A magnetic field is represented by the lines of magnetic induction.

6) The lines of magnetic induction are closed curve (i.e. continuous curves, without any indication of starting or ending point).
7) If the lines of magnetic induction are a region is crowded together, the magnetic field strength in that region will be strong. If the lines of magnetic induction are a region are far apart, there the magnetic field strength is weak.
8) The lines of magnetic induction far a uniform magnetic field are parallel and equidistant. The magnitude and direction of magnetic field induction in a uniform magnetic field are the same at every point in this field.
9) S.I. unit of magnetic field induction is tesla (denoted by T) or weber/meter2 (denoted by Wb/m2). The c.g.s e.m. unit of magnetic field induction is gauss (denoted by G) or maxwell/centimeter square.

### Nature of the magnetic field

1) A straight current (i.e. linear conductor carrying current) produces a circular magnetic field i.e. the magnetic lines of forces are in the form of concentric circles with the conductor as centre.
2) A circular current (i.e. a circular coil carrying current) behaves as a magnetic shell, the polarity of which depends upon the direction of current in the circular coil. The magnetic lines of force due to the circular current are circular near the circular coil but are straight and parallel at the centre of the circular coil.
3) The magnetic lines of force due to a current carrying solenoid are similar to those due to a bar magnet.

### Magnetic field at the centre

Magnetic field induction at the centre of a circular coil of radius r, having n insulated turns; carrying current I in S.I. unit is given by: B = µ0/4π * a π n I/r = µ0nI/2r The magnetic field due to circular coil is uniform at the centre of the coil and non-uniform near the circular coil. It means the magnetic lines of induction are straight and parallel near the centre of circular coil and in the form of concentric circles near the coil. The direction of magnetic field conduction at the centre of circular coil carrying current is given by Right Harm Palm Rule. According to which the direction of B is perpendicular to the plane of coil downwards for the clockwise current and perpendicular to the plane of coil upwards for the anticlockwise current.

### Ampere’s law

1) It states that the line integral of magnetic field induction B around any closed path in vacuum is equal to  µ0 times the total current threading the closed path i.e. ∫B .dl = µ0I
2) It is analogous to Guass’s law in electrostatics.

### Solenoid

1) A solenoid consists of an insulated long wire closely wound in the form of a helix. Its length is very large as compared to its diameter.
2) Magnetic field induction at a point well inside the solenoid of length l, having N turns carrying current I is given by B = µ0 NI/L
3) Magnetic field induction at a point on one end of the solenoid carrying current is B = µ0NI/ 2L
4) Magnetic field induction at a point on the axis of the solenoid having n turns per unit length in general is given by B= µ0nI [cosѳ1- cosѳ2].
5) The magnetic field induction at a point outside the curved face of the solenoid carrying current is zero.
6) The magnetic lines of induction due to current carrying solenoid resemble exactly with those of a bar magnet.

### Cyclotron frequency

When the frequency of oscillations of a charged particle in cyclotron becomes equal to the frequency of the oscillation electric field applied, then the frequency of the particle is called the cyclotron frequency, which is given by v = Bq/2 µm

### Torque on a coil in a magnetic field

1) If a coil of area A, having n insulated turns, carrying current I, when suspended in a uniform magnetic field of induction B, it experiences a torque, given by Ԏ = n I B A sin α =M B sin α, where M = nIA. Here α is the angle which the normal drawn on the plane of the coil makes with the direction of magnetic field.
2) If the plane of the coil is perpendicular to the direction of magnetic field i.e. α = 0˚ then Ԏ = 0 ( i.e. minimum)
3) If the plane of the coil is parallel to the direction of magnetic field i.e. α =90˚ then Ԏ = n I B A ( i.e. maxiimum)