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Question

# A magnetic field set up using Helmholtz coils (described below) is uniform in a small region and has a magnitude of 0.75T. 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 15kV 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 9.0×10−5Vm−1, make a simple guess as to what the beam contains. Why is the answer not unique?Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by, B=0.72μ0NIR.[Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils].

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Solution

## Kinetic energy of the electron =eVunder equilibrium conditions, 12mv2=eV−(1)Since the particle remains undeflected by electric and magnetic field, we can infer that the electric field is balancing the magnetic field.so, eE=evB−(2)From (1) and (2),e/m=E2/2VB2=4.8×107 C/kgThis 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.

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