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www.GOALias.blogspot.comPhysicsNow the current enclosed I eis not I, but is less than this value.Since the current distribution is uniform, the current enclosed is,Ie2⎛ πr⎞I⎝πa⎠= ⎜ 2 ⎟Ir=a22Using Ampere’s law,IrB(2 ðr)= µa0 22⎛ µ0I⎞B = ⎜ r2⎝⎟2ða⎠B ∝ r (r < a)[4.19(b)]EXAMPLE 4.8FIGURE 4.16Figure (4.16) shows a plot of the magnitude of B with distance rfrom the centre of the wire. The direction of the field is tangential tothe respective circular loop (1 or 2) and given by the right-handrule described earlier in this section.This example possesses the required symmetry so that Ampere’slaw can be applied readily.It should be noted that while Ampere’s circuital law holds for anyloop, it may not always facilitate an evaluation of the magnetic field inevery case. For example, for the case of the circular loop discussed inSection 4.6, it cannot be applied to extract the simple expressionB = µ 0I/2R [Eq. (4.16)] for the field at the centre of the loop. However,there exists a large number of situations of high symmetry where the lawcan be conveniently applied. We shall use it in the next section to calculatethe magnetic field produced by two commonly used and very usefulmagnetic systems: the solenoid and the toroid.1504.8 THE SOLENOID AND THE TOROIDThe solenoid and the toroid are two pieces of equipment which generatemagnetic fields. The television uses the solenoid to generate magneticfields needed. The synchrotron uses a combination of both to generatethe high magnetic fields required. In both, solenoid and toroid, we comeacross a situation of high symmetry where Ampere’s law can beconveniently applied.