Class 12 Physics
CBSE and UP Board
Moving Charges and Magnetism
Chapter-4 Exercise 4.20
Additional Exercise
A magnetic field set up using Helmholtz coils (described in Exercise 4.16) is uniform in a small region and has a magnitude of 0.75 T. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through 15 kV enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is 9.0 × 10⁻⁵ V m⁻¹, make a simple guess as to what the beam contains. Why is the answer not unique?
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Magnetic field, B = 0.75 T
Accelerating voltage, V = 15 kV = 15 x 103 V
Electrostatic field, E = 9 x 105 V m⁻¹
Mass of the electron = m,
Charge of the electron = e,
Velocity of the electron = v
Kinetic energy of the electron = eV
=>1/2 x mv2 =eV
Therefore e/m = v²/2V———————- Eq-1
Since the particle remains un-deflected by electric and magnetic fields, we can infer that the electric field is balancing the magnetic field.
Therefore eE =evB
v = E/B—————————–Eq-2
Putting Eq-2 in equation 1, we get
e/m = 1/2 x (E/B)² /V = E²/2VB²
= (9 x 105 )²/[2 x 15000 x (0.75)²]
=4.8 x 10⁷ C/Kg
This value of specific charge e/m is equal to the value of deuteron or deuterium ions. This is not a unique answer. Other possible answers are He++ Li++, etc