NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field
Force on a Moving Charge in Uniform Magnetic Field
Force on a Moving Charge in Uniform Magnetic Field
The magnetic force Fm acting on a charge q moving with a velocity v in magnetic field B is given by
Fm = qvB.
The direction of force Fm is given by rule of vector product.
The force Fm is zero, if either B = 0 or
v = 0 or (c) q = 0 i.e. the particle is neutral particle or θ = 0° or 180° i.e. motion of charged particle is parallel or anti-parallel to the magnetic field.
The force Fm is maximum having a value θ = 90° i.e. charged particle is moving in a direction perpendicular to that of magnetic field.
Thus, magnetic field B may be defined by the relation
Thus, SI unit 1 T =1NA-Im-2.
Motion of a Charged Particle in a Uniform Magnetic Field
If a charge particle enters a uniform magnetic field B with a velocity v in a direction perpendicular to that of B θ = 90° then the charged particle experiences a force Fm = qvB. . Under its influence the particle describes a circular path, such that
Radius of circular path 
In general
where, p = mv = momentum of charged particle,
K = kinetic energy of charged particle and
V = accelerating potential difference.
The period of revolution of charged particle
Moreover, pitch (the linear distance travelled during one complete revolution) of helical path is given by
If the direction of a v is parallel or anti-parallel to B, 
and therefore, F = 0. Hence, the trajectory of the particle is a straight line.
If the velocity of the charged particle is not perpendicular to the field, we will break the velocity in parallel 
and perpendicular 
components.
Cyclotron
It is a device used to accelerate positively charged particles e.g. proton, deuteron, a-particle and other heavy ions to high energy of 100 MeV or more. It utilises the principle that an electric field accelerates the charged particles and a normal magnetic field keeps them revolving in circular orbits or constant frequency.
For continuous acceleration the cyclotron frequency v is arranged, so that during the time ion completes a semi-circular path in a dee, direction of electric field is just reversed. Cyclotron frequency
Maximum energy gained by the charged particle 
where r = maximum radius of the circular path followed by the positive ion.
Maximum energy obtained by the particle is in the form of kinetic energy.