Faraday\'s law: Betatron accelerator. A betatron accelerator consists of two lar
ID: 1270600 • Letter: F
Question
Faraday's law: Betatron accelerator. A betatron accelerator consists of two large cylindrical electromagnets. The magnetic field between the magnets points along their common axis (the 2-axis). The magnetic field in the region of interest is essentially uniform but varies in time as where Bo is the Final value attained by the magnetic held once it is turned on and r is the time scale for the magnetic field to reach its final value, (a) What is the magnetic flux through the imaginary loop of radius r at time t shown in figure 5? (b) What is the line integral of the electric field around the loop? (c) What is the tangential electric field at a distance r from the betatron axis? Figure 5: Betatron accelerator showing the magnets and magnetic field (left), the location of the loop of radius r (center) and another view of the loop (right).Explanation / Answer
(a.) Flux ?(t)=B.dS = Bo[1-exp(-t/T)].?r^2 = Bo?r^2[1-exp(-t/T)]
(b.) Zero. Because the cyclic (or closed) integral of electric field is zero.
(c.) Zero. Because the electric field due to a current loop is always directed along the axis of the ring. The tangential components cancel out each other.
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