4.20 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?
4.20 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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1 Answer
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4.20 Magnetic field, B = 0.75 T
Accelerating voltage, V = 15 kV = 15 V
Electrostatic field, E = 9.0 V/m
Let the mass of electron = m, Charge of the electron = e, Velocity of the electron = v
Then kinetic energy of the electron = eV
m = eV or = ………….(1)
Since the particle remains un-deflected by electric and magnetic field, we can infer that the electric field is balancing the magnetic field.
Hence eE = evB or v = ………(2)
Combining equation (1) and (2), we get
= = = 48 C/kg
This value of specific charge e/m is equal to the value of deuteron or deuterium ions. This is not a uniqu
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