A circular conducting loop is held ?xed in a uniform magnetic ?eld that varies i

Question

A circular conducting loop is held ?xed in
a uniform magnetic ?eld that varies in time
according to B(t) = B0 exp(?a t) where t is
in s, a is in s
?1
and B is the ?eld strength in
T at t = 0. At t = 0, the emf induced in the
loop is 0.0577 V . At t = 3.57 s, the emf is
0.0167 V.
Find a.
Answer in units of s
?1

Explanation / Answer

dB/dt = -a*Bo exp(-at) The flux = pi*r^2*B(t) so the change in flux d (flux) / dt = pi*r^2*dB/dt=-pi*r^2*a*Bo exp (-at) = E, the emf Now you have three unknowns, a, r and Bo. You can set up two equations with the conditions you have: i. t=0 --> a*Bo*pi*r^2=0.0792 ii. t=2.79 --> a*Bo*pi*r^2 exp(-a*2.79)=0.0375 Solve for a. The easiest way is to divide equation ii by equation i, so after everything cancels, you get exp (-a*2.79)=0.0375/0.0792 Solve that for a by taking the ln.

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