We have already studied about thermal effects of current and now in the present chapter we are studied about magnetic effect of current.
Earlier it was believe that there is no connection between electric and magnetic force and both of them are completely different.
But in 1820 Oersted showed that the electric current through a wire deflect the magnetic needle placed near the wire and the direction of deflection of needle is reversed if we reverse the direction of current in the wire.
So, Oersted's experiments establishes that a magnetic field is associated with current carrying wire.
Again if we a magnetic needle near a bar magnet it gets deflected and rests in some other direction.
This needle experiences the torque which turn the needle to a definite direction.
Thus, the region near the bar magnet or current carrying where magnetic needle experience and suffer deflection is called magnetic field.
The Magnetic Field
We all ready know that a stationery charges gets up a electric field E in the space surrounding it and this electric field exerts a force F=q_{0}E on the test charge q_{0} placed in magnetic field.
Similarly we can describe the interaction of moving charges that, a moving charge exert a magnetic field in the space surrounding it and this magnetic field exert a force on the moving charge.
Like electric field, magnetic field is also a vector quantity and is represented by symbol B
Like electric field force which depend on the magnitude of charge and electric field, magnetic force is proportional to the magnitude of charge and the strength of magnetic field.
Apart from its dependence on magnitude of charge and magnetic field strength magnetic force also depends on velocity of the particle.
The magnitude magnetic force increase with increase in speed of charged particle.
Direction of magnetic force depends on direction of magnetic field B and velocity v of the charged particle.
The direction of magnetic force is not along the direction of magnetic field but direction of force is always perpendicular to direction of both magnetic field B and velocity v
Test charge of magnitude q_{0} is moving with velocity v through a point P in magnetic field B experience a deflecting force F defined by a equation F=qv X B
As mentioned earlier this force on charged particle is perpendicular to the plane formed by v and B and its direction is determined right hand thumb rule.
When moving charge is positive the direction of force F is the direction of advancement of right hand screw whose axis is perpendicular to the plane formed by v and B.
Direction of force would be opposite to the direction of advancement of right hand screw for negative charge moving in same direction.
Magnitude of force on charged particle is
$ F=q_0 vBsin \theta$
where θ is the angle between v and B.
If v and B are at right angle to each other i.e. θ=90 then force acting on the particle would be maximum and is given by
$F_{max}=q_0 vB$ ----(3)
When θ=180 or θ=0 i.e. v is parallel or anti parallel to B then force acting on the particle would be zero.
Again from equation 2 if the velocity of the particle in the magnetic field is zero i.e., particle is stationery in magnetic field then it does not experience any force.
SI unit of strength of magnetic field is Tesla (T). It can be defined as follows
$ B=\frac {F}{qvsin \theta}$
for F=1N,q=1C and v=1m/s and θ=90
1T=1NA^{-1}m^{-1}
Thus if a charge of 1C when moving with velocity of 1 m/s along the direction perpendicular to the magnetic field experiences a force of 1N then magnitude of field at that point is equal to 1 Tesla (1T).
Another SI unit of magnetic field is Weber/m^{2} Thus
1 Wb-m^{-2}=1T=1NA^{-1}m^{-1} In CGS system, the magnetic field is expressed in 'gauss'. And 1T= 10^{4} gauss. Dimension formula of magnetic field (B) is [MT^{-2}A^{-1}]
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