1 Magnetic  filed induction  near  an infinitely long straight conductor :

\(B=\frac {\mu_0 i} {2\pi r}\)

i = current through the conductor

r = perpendicular distance 

2 From  Bio-Savart's law, the intensity of magnetic induction  due to the element  of a current-carrying conductor  is 

\(dB=\frac {\mu_0 } {4\pi} \frac {idl\sin \theta} {r^2} (Wb/m^2)\)

\(\mu_0\)  =  permeability of free space

i  = current through the conductor

dl= length of an element  in the conductor 

r = distance from the element 

\(\theta\)  = angle between dl  and r
 

The vector form of biot-savant's law is  \(\overline{dB}=\frac {\mu_0} {4\pi}.\frac {i(\overline{dl}\times \overline{r})} {r^3}\)

The  magnetic field induction at a point on the axial line of a current-carrying circular coil is 

\(B=\frac {\mu_0nir^2} {2(r^2+x^2)^{\frac 32 }}\)

n = number of turns of the coil

i = strength of current 

r = radius of the coil

x = distance to the point  from the centre of the coil 

At the center of a coil  \(B_c=\frac {\mu_0 ni} {2r}\)

The magnetic moment of a circular  coil of n turns to carry current i with radius r is  \(M=niA=ni\pi r^2\)

Force on a moving charge in a magnetic field is 

\(\overline{F}=q(\vec{v}\times \vec{B})\)

\(\vec{F}= qvB\sin \theta\)

The force acting on a current-carrying conductor in a magnetic field is

\(\overline{F}=i(\vec{l}\times \vec{B})\)

\(F=ilB\sin \theta\)

B= magnetic field induction 

i = current through the conductor 

l = length of the conductor 

\(\theta\) = angle between  \(\overline{l}\)  and  \(\overline{B}\)

This force acts right angles to \(\overline{B}\)  and \(\overline{V}\).its acts as centripetal force and the path of the particle will be circular. The radius of the circular path is given by

\(r=\frac {mv} {Bq} ;r=\frac {p} {Bq}\)    \(\Big( Bqv=\frac {mv^2} {r}\Big)\)

1. The space in the surroundings of a magnet or a current-carrying conductor in which its magnetic influence can be experienced is called magnetic field. Its SI unit is Tesla (T).
2. Oersted experimentally demonstrated that the current-carrying conductor produces magnetic field around it.

When key K is closed, then deflection occurs in the compass needle and vice-versa,

 Biot-Savart’s Law According to this law, the magnetic field due to small; current-carrying element dl at any nearby point P is given by

Oersted's Law

In April 1820, Hans Christian Oersted discovered that flow of current in a wire can deflect nearby magnetic compass needle.

Force between parallel current carrying wires

\(F=\ \frac{\mu_0\ i_1\ i_2}{2\ \pi\ d}\)

Torque experienced by a loop in a uniform magnetic field

\(\vec T=\ \vec M\ \times\ \vec B\)

\(\vec T=\ N\ B\ i\ A\)

Definition of Ampere

If two parallel wires carrying same current are kept 1 m apart, if experience a force \(F=\ 2\ \times 10^{-7}\ N,\) then current = 1 A in each wire.

Sensitivity

Voltage Sensitivity = NBA / CG 

Current Sensitivity = NBA / C

Galvanometer

\(Ammeter\)

\(S=\ \frac{I_g}{I\ -\ I_g}\ G\)

\(Voltmeter\)

\(R=\ \frac{V}{I_g}\ -\ G\)