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NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field

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
NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 1
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 NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 2
In general
NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 3
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
NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 4
NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 5
Moreover, pitch (the linear distance travelled during one complete revolution) of helical path is given by
NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 6
If the direction of a v is parallel or anti-parallel to B, NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 7 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 NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 8and perpendicular NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 9 components.
NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 10

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
NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 11
Maximum energy gained by the charged particle NEET Physics Notes Magnetic Effects of Current-Force on a Moving Charge in Uniform Magnetic Field 12
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.

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