a) UsingFaraday’s Law, find the formula for the induced emf as afunction of time

Question

a)      UsingFaraday’s Law, find the formula for the induced emf as afunction of time (5 points).

b)      Calculateinduced emf for t = 0, t =0.10 s, t = 0.20 s (2points).

c)      Using thevalues you calculated in (b), plot the induced emf as a function oft (2 points).

d)      Find the powerdissipating in R at t = 0.10 s (2 points).

e)      Sate the Lenzrule and use it to find which way the current will flow in R: froma to b or from b to a? Explain based on Lenz rule [No creditfor guessing without an explanation] (3points).

Explanation / Answer

(a) induced emf = -d(BA)/dt =   -B dA/dt =   -B d(a2)/dt =   -B 2a da/dt   = .               = -B 2(ao - ct) ( -c)     .    inducedemf =   2 c B (ao - ct) . This is the forumla as an algebraic expression. If they wantnumbers, then   B = 0.45   c =2.0    ao = 0.75   and .     induced emf = 2*2.0*0.45 (0.75- 2.0t) =    1.80 (0.75 - 2.0t)      in Volts . (b)   t          induced emf .         0              1.35 .        0.10          0.99 .       0.20           0.63 . (c)   plot the points... it should be a straightline . (d) power dissipated = V2 /R = 0.992 / 25 =   0.0392 Watts =   39.2 mW . (e) Lenz Law states that the direction of the inducedcurrent will be to oppose the change in the magnetic flux. The fluxis into the page and decreases as the area decreases. So thecurrent will be induced such that it will create magnetic field outof the page. Using the right hand rule, this means the inducedcurrent flows counterclockwise around the loop... and so it passes from b to a through the resistor. . (b)   t          induced emf .         0              1.35 .        0.10          0.99 .       0.20           0.63 . (c)   plot the points... it should be a straightline . (d) power dissipated = V2 /R = 0.992 / 25 =   0.0392 Watts =   39.2 mW . (e) Lenz Law states that the direction of the inducedcurrent will be to oppose the change in the magnetic flux. The fluxis into the page and decreases as the area decreases. So thecurrent will be induced such that it will create magnetic field outof the page. Using the right hand rule, this means the inducedcurrent flows counterclockwise around the loop... and so it passes from b to a through the resistor.

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