A way to produce a fairly uniform magnetic field over a large accessible region

Question

A way to produce a fairly uniform magnetic field over a large accessible region is with a pair of identical circular loops of wire that share the same axis and are physically parallel to each other, but whose centers are a certain distance apart. Each carries equal current in the same direction. Consider the case in which the loops are are both parallel to the y-z plane, their common axis being the x-axis, and with diameters of 48.0cm . Each carries a current of 4.30A , and they are 30.0cmapart and equidistant from the origin. Suppose a particle of charge +e, where e is the fundamental charge, is at the origin, moving in the +y-direction at speed 2950m/s .

Explanation / Answer

magnetic field B due to each of the wire is B = uoi/2R

so

B = (4*3.14e-7 * 4.3)/(2* 0.24)

B1 = B2 = 1.12 uT

Bnet = B1+ B2 = 2B = 2.25 e-5 T

so

magnetic force on the charge F = qvB

F = 1.6 e-19 * 2150 * 2.25 e-5

F   = 7.74 *10^-21 N

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