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].