Calculating EMF Induced Current in a Circular Loop of Wire

In summary, the problem is calculating the induced emf in a circular loop of wire with a diameter of 23 cm, when the magnetic field perpendicular to the loop changes from +0.52 T to -0.45 T in 175 ms. Using the equation for induced emf, we can calculate the emf to be 5.54 V. The negative sign in front of the equation is necessary and the flux is the product of the magnetic field and the area perpendicular to the field lines. This is why the induced emf changes as the loop turns in a constant magnetic field.
  • #1
metalmagik
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0

Homework Statement



The magnetic field perpendicular to a circular loop of wire 23 cm in diameter is changed from +0.52 T to -0.45 T in 175 ms, where + means the field points away from an observer and - toward the observer.


Homework Equations



(pardon me with the equations, I am LaTeX challenged.)

emf = N x (delta flux)/(delta time)

emf = Blv

The Attempt at a Solution



emf = (1) (.97)/(.175)

emf = 5.54 V

I have seen this equation with a negative infront...does this need to be put in the answer? This is for a WebAssign. I apologize for the rushed manner in which I posted this, but I have a ton of other work to do. Any help on this is greatly appreciated.
 
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  • #2
[tex]V = -N \frac{d\phi}{dt}[/tex]

So first, yes, there is a negative sign in front. Second, what is the equation that relates the B field to the flux [tex]\phi[/tex] ?
 
  • #3
The induced emf in a coil also depends on the area it presents to the changing manetic field through it. So the flux is the product of the magnetic field and the area perpendicular to the magnetic field lines. That is why the induced emf changes as the coils of a generator turns in the constant magnetic field - the area they present to the magnetic field lines changes as they revolve in the field.
 

1. How is the EMF induced current calculated in a circular loop of wire?

The EMF (electromotive force) induced in a circular loop of wire is calculated using Faraday's law of induction: EMF = -N(dΦ/dt), where N is the number of turns in the loop and dΦ/dt is the rate of change of magnetic flux through the loop. This equation quantifies the amount of induced voltage in the loop, which is directly proportional to the induced current.

2. What factors affect the magnitude of the induced current?

The magnitude of the induced current in a circular loop of wire is affected by several factors, including the strength of the magnetic field, the area of the loop, the number of turns in the loop, and the rate of change of the magnetic flux through the loop. Additionally, the resistance of the wire and the circuit it is connected to can also impact the magnitude of the induced current.

3. How is the direction of the induced current determined?

The direction of the induced current in a circular loop of wire is determined by Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux through the loop. This means that if the magnetic flux is increasing, the induced current will flow in one direction, and if the magnetic flux is decreasing, the induced current will flow in the opposite direction.

4. Can the induced current be increased?

Yes, the induced current in a circular loop of wire can be increased by increasing the strength of the magnetic field, the number of turns in the loop, or the rate of change of the magnetic flux through the loop. Additionally, using a material with lower resistance for the wire or connecting the loop to a circuit with lower resistance can also increase the induced current.

5. What is the significance of calculating the induced current in a circular loop of wire?

Calculating the induced current in a circular loop of wire is important in understanding and predicting the behavior of electromagnetic systems. It is used in various applications, such as generators, motors, transformers, and other electrical devices. It also helps in studying the relationship between electricity and magnetism and is a fundamental concept in electromagnetism.

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