What is the motional emf of the loop at time t = 0.032 s?

AI Thread Summary
The discussion centers on calculating the motional electromotive force (emf) of a conducting loop at time t = 0.032 s, as it enters a magnetic field. The loop consists of two squares, with a given magnetic field strength of 1.2 T and a constant speed of 40 cm/s. The attempt to calculate the induced current involves determining the area of the loop entering the field and applying the formula for emf, but the initial calculations yield incorrect results. The user realizes that the correct approach involves using the relationship emf = B * v * L, where L is the distance traveled in the magnetic field over time. The discussion highlights the need for careful application of the formulas to achieve the correct answer.
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Homework Statement



A conducting loop is made in the form of two squares of sides s1 = 3.8cm and s2 = 6 cm as shown. At time t = 0, the loop enters a region of length L = 18.6 cm that contains a uniform magnetic field B = 1.2 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 40 cm/s. The resistance of the loop is R = 2.8 O.

At time t = t1 = 0.032 s, what is I1, the induced current in the loop? I1 is defined to be positive if it is in the counterclockwise direction.

Hint: The induced emf in the loop is not equal to the flux through the loop, but rather the time derivative of the flux through the loop.

Homework Equations


Velocity = distance/time
emf = -B.dA/dt

The Attempt at a Solution


total moving length =L+s1+s2=28.4cm

time=D/v= 28.4/40 =0.71s

At t=0.035s , the distance is 1.4 cm w
distance=velocity.time = 40.(0.035) = 1.4cm

this distance we can take as entering length of the loop.
For L=1.4cm, Area at time(dA/dt) = L*W = 1.4(3.8)cm^2 = 5.32*10^-4 m^2

e.m.f in the loop of this area:
e=-B.dA/dt=1.2*5.32*10^-4 v = 6.384 *10^-4 v
the induced current at this time i=e/R = 6.384*10^-4/2.8 (R=2.8 ohm given) = 0.228 mA

But, its not the correct answer> Help! What am I doing wrong?
 
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EDiT:

To do this problem, I know that we first have to find motional emf of the loop at time t =0.032 s? I also know that emf= BxvL where v is the velocity where L= velocity*time

But when I try to plug in numbers I'm getting a wrong answer.
emf= 1.2*.4*(.4*.032) = 0.006144 Volts
 
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