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

In summary, a conducting loop with a length of 18.6 cm and a uniform magnetic field of 1.2 T is moving at a constant speed of 40 cm/s. At time t = 0.032 s, the induced emf in the loop is 0.006144 V and the induced current is 0.228 mA in the counterclockwise direction. The total moving length of the loop is 28.4 cm and the loop has a resistance of 2.8 ohms.
  • #1
hime
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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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  • #2
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
 

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

1. What is Ampere's Law and how does it relate to electromagnetism?

Ampere's Law is a fundamental principle in electromagnetism that describes the relationship between electric currents and magnetic fields. It states that the magnetic field created by a current-carrying wire is directly proportional to the current flowing through the wire and the distance from the wire.

2. Can you explain the concept of motional EMF and how it is related to Ampere's Law?

Motional EMF refers to the electromotive force generated in a conductor when it moves through a magnetic field. This phenomenon is based on Ampere's Law, as the motion of the conductor creates a changing magnetic field, which in turn induces an electric field and an EMF in the conductor.

3. How is Ampere's Law used in practical applications?

Ampere's Law is used in a variety of practical applications, such as in the design of electric motors, generators, and transformers. It is also essential in understanding the behavior of electromagnetic waves and in the development of technologies like MRI machines and particle accelerators.

4. What are some key equations and variables involved in Ampere's Law?

The key equation in Ampere's Law is B = μ0I/2πr, where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the current-carrying wire. Other important variables include the length and shape of the current path, as well as the strength and direction of the current.

5. Are there any limitations or exceptions to Ampere's Law?

While Ampere's Law is a fundamental principle in electromagnetism, it does have some limitations and exceptions. It is only valid for steady currents and does not account for the effects of changing electric fields. In addition, it does not apply to all situations, such as when the current path is not a closed loop or when there are varying magnetic fields present.

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