Figure (a) shows a circuit consisting of an ideal battery with emf E = 6.31 mu V

Question

Figure (a) shows a circuit consisting of an ideal battery with emf E = 6.31 mu V, a resistance R, and a small wire loop of area 5.6 cm^2. For the time interval t = 24 s to t = 48 s, an external magnetic Field is set up throughout the loop. The field is uniform, its direction is into the page in Figure (a), and the field magnitude is given by B = at, where B is in teslas, a is a constant, and t is in seconds. Figure (b) gives the current j in the circuit before, during, and after the external field is set up. The vertical axis scale is set by I_s = 3.0 mA, and the horizontal axis scale is set by t_s = 72 s. Find a. Number ________ Units The number of significant digits is set to 2; the tolerance is +/-5%

Explanation / Answer

from t = 0 to t = 24 s

current Is = e/R = 6.31/R = 3*10^-3

R = 6.31/(3*10^-3) = 2103 ohm

magnetic flux = B*A = at*A

emf induced , emf = rate of change in flux

emf = a*A

induced current Id = a*A/R

Id = Is - Is/3

Id = 2 mA

2*10^-3 = a*5.6*10^-4 /2103.3

a = 7511.8 T/s

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