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

is zero in such cases.
Note:
The equation
implies 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:


The direction of the force can be given by right hand screw rule or Fleming's left hand rule.
Note:
1) If = 0o or 180o then F = 0 (minimum)
2) If = 90o then F = I x l x B (maximum)





