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Q.NO
CBSE;Class XII;Physics;Moving Charges and Magnetism;Motion of a
Charge in Combined Electric and Magnetic Fields
Question
Solution
Consider a region in which a uniform magnetic field of magnetic
induction B and uniform electric field of strength E exist. Let a
particle with charge q move in this region with a velocity v
perpendicular to both electric and magnetic fields. Here, the
electric field, magnetic field and the velocity of the charged
particle are mutually perpendicular to each other.
When the charged particle moves in both electric and magnetic
fields as shown, the particle experiences a Lorentz force, F =
Felectric + Fmagnetic = q (E = v x B)
If the magnitudes of electric field strength and magnetic field
strength are adjusted such that the magnitudes of the two forces
are equal then the net force acting on the charged particle is zero.
This principle is used to select the particles to be projected into
the fields based on their velocity. So the crossed electric field and
the magnetic fields are called velocity selectors.
The particles, whose magnitude of velocity is equal to the ratio of
E to B, pass through the combination of electric field and magnetic
field without deviation and the remaining particles whose velocity
is not equal to the ratio of E to B, deviate on either side of the
electric field. This principle is used in the mass spectrometer and
particle accelerators.
The mass spectrometer is a device used to separate charged
particles based on their charge to mass ratio. Particle accelerators
are used to accelerate particles to very high energy.
A cyclotron is a particle accelerator which accelerates a charged
particle. It consists of two hollow, flat, semicircular metal disc-like
containers called D1 and D2. These two Ds are separated by a
narrow, parallel gap. These two Ds are connected to a highfrequency oscillator which produces an alternating voltage. This
alternating voltage establishes an alternating electric field
between the two Ds once from D1 to D2 and then from D2 to D1.
This electric field between the Ds accelerates the charged particle
when it passes through the gap between the Ds.
When a charged particle enters a D, it moves in a circular path
with constant speed because inside the D, it is influenced only by
the magnetic field. Inside the D, the electric field is zero due to the
shielding effect.
The cyclotron frequency is independent of the speed of the
charged particle and radius of the circular path.
Cyclotrons are used to bombard nuclei with energetic particles by
accelerating them in Cyclotrons, and to study nuclear reactions.