- Introduction
- |
- The Magnetic Field
- |
- Lorentz Force
- |
- Motion of Charged Particle in The Magnetic Field
- |
- Cyclotron
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- Magnetic force on a current carrying wire
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- Torque on a current carrying rectangular loop in a magnetic field

- We have allready 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 assoiated with current carrying wire.

- Again if we a magnetic needlle near a bar magnet it gets deflectid and rests in some other direction.

- This needle experiences the tourque which turn the needle to a definite direction.

- Thus, the reagion near the bar magnet or current carrying where magnetic needle experience and suffer deflection is called 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 intraction of moving charges that, a moving charge excert a magnetic field in the space surrounding it and this magnetic field exert a force on the moving charge.

- Like electric field, magntic 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 propotional 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 magnetc field B and velocity
**v**of the chared particle.

- The direction of magnetic force is not alonge 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**=q**v**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 advance of hand screw whose axis is perpendicular to the plane formed by**v**and**B**.

- Direction of force would be opposit to the direction of advance screw for negative charge moving in same direction.

- Magnitude of force on charged particle is

F=q_{0}vBsinθ

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 antiparallel to B then froce acting on the particle would be zero.

- Again from equation 2 if the velocity of the palticle 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=F/qvsinθ

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 1m/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. Dimention formula of magnetic field (B) is [MT^{-2}A^{-1}]

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