Magnetic Field

If a charged particle is projected in a magnetic field, in general, it experiences a magnetic force. By projecting the particle in different direction from the same point P with different speeds, we can observe the following facts about the magnetic field force.

a.       Force experienced by the moving charge is directly proportional to the magnitude of the charge i.e.

F α q

b.       Force experienced by the moving charge is directly proportional to the component of velocity perpendicular to the direction of magnetic field i.e.

F α v sinθ

c.       The magnitude of the force F is directly proportional to the magnitude of the magnetic field applied i.e.

F α B

On combining all factors we get,

F = kq v sinθ B

Here k=1 is proportionality constant. F= q v sinθ B. Here we can see that v and B follows the vector product hence force is perpendicular to v and B. Direction of the force can be can by Right Handed Screw Rule or Right Hand Rule.

  

By measuring the magnetic force F acting on a charge q moving at a speed v, we can obtain B. If v=1, q=1 and sinθ =1 or θ=90º then F = 1x 1x B x 1 =B

Thus the magnetic field induction at a point in the field is equal to the force experienced by a unit charge moving with a unit velocity perpendicular to the direction of magnetic field at that point.

Special Cases

a.       If θ =0º or 180º the F = q v Bsin(0) = 0. Its means, a charged particle moving parallel to the direction of magnetic field, does not experience any force.

b.      If θ =90º or 180º the F = q v Bsin(90) = qvB (maximum force). Its means, a charged particle moving along a perpendicular to the direction of magnetic field, it experiences maximum force.

c.       If v =0, then F=q v sinθ B = 0. It means, a charged particle is at rest in a magnetic field, it experiences maximum force. It experiences no force.

UNIT OF MAGNETIC FIELD B

SI unit of magnetic field is tesla (T) or Weber /meter²

1T = 1NA^-1m^-1

1 Gauss = 10^-4 T

Dimensions of B = [MA^-1T^-2]

We have a magnetic field of the order of 10^-5 T near to earth surface

Magnetic field is also called as Magnetic Induction or Magnetic Flux Density.