Lorentz Force

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The force experienced by a charged particle moving in space where both electric and magnetic field exist is called lorentz force. The lorentz force is therefore the vector sum of force due to electric field and the force due to magnetic field. Mathematically

or

Definition of 1 Tesla

The magnetic field induction at a point is said to be one tesla if a charge of 1 coulomb while moving at right angles to a magnetic field with a velocity of 1m/sec experiences a force of 1N at that point.

Magnetic Force on a Moving Charge

2) When the charges move parallel or anti-parallel to the magnetic field, q = 0^o or 180^o, the is zero in such cases.

4) For charges of opposite sign the force acts in a direction opposite to that of positive charges.

Note:

The equationimplies that since are always perpendicular, the magnetic force does no work. [This means the force cannot change the speed of the particle].

In such a case the kinetic energy remains constant. The work-energy theorem implies that work is said to be done by a force if it brings about a change in its speed or kinetic energy.

It can be seen that

 

 

Therefore it follows that,

Here, K.E. = constant

Magnetic Force on a Current Carrying Conductor in an Uniform Magnetic Field

A moving charge in a magnetic field experiences forces. An electric current in a conductor is due to drifting of free electrons in a definite direction in the conductor. When such a current carrying conductor is placed in a uniform magnetic field, each free electron experiences a force. Since free electrons are constrained in the conductor, the conductor itself experiences a force. Hence a current carrying conductor placed in a magnetic field experiences a force.

The illustration below shows a force experienced by a current carrying conductor.

Consider a conductor PQ of length l and area of cross section A, carrying current I placed in a uniform field   (represented as x i.e., lines of force go into the paper)

Then the magnetic Lorentz force on a electron would be

If n be the number density, then number of free electrons will be nAl.

The total force on conductor due to free electrons:

where q is the angle between l and B.

The direction of the force can be given by right hand screw rule or Fleming's left hand rule.

Note:

1) If = 0^o or 180^o then F = 0 (minimum)

2) If = 90^o then F = I x l x B (maximum)