Faraday's law -- Confusion about which Area to use in calculations

In summary, the confusion surrounding Faraday's law often stems from the appropriate choice of area when calculating induced electromotive force (EMF). Different interpretations of the area involved, such as the surface area of the loop or the area through which the magnetic flux changes, can lead to discrepancies in results. Clarifying the context and the specific setup of the electromagnetic situation is essential for accurate calculations and understanding of the law's application.
  • #1
yymm
5
0
Homework Statement
Since magnetic flux(phi) is given by BA, is the A referring to the area that is generating the flux or is it referring to the area that's experiencing the change in flux? For example, in the first question, area would clearly be referring to the area of the loop right, but in the second example, the solutions substituted A=(0.02^2)pi, which is the area of the solenoid that is generating the flux? Doesn't it make more sense to use A as the area for the area of the loop thats experiencing the flux, which is (0.06^2)pi?
Relevant Equations
Ndphi/dt=emf
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  • #2
The flux is not BA in general. Only when the magnetic field is uniform and perpendicular to the surface the formula for flux has this simple form. Uniform means the same value and direction for all points of the area considered.
Do you think that this condition is satisfied for the flux throug the ring? Is the magnetic field (produced by the solenoid) uniform across the area of the ring?
 
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  • #3
yymm said:
Doesn't it make more sense to use A as the area for the area of the loop thats experiencing the flux, which is (0.06^2)pi?
Only the area of the loop that is equal to the cross sectional area of the solenoid has magnetic flux through it. Outside the solenoid the magnetic field is zero therefore the flux through the rest of the loop's area is zero. That makes sense, no?
 
  • #4
kuruman said:
Only the area of the loop that is equal to the cross sectional area of the solenoid has magnetic flux through it. Outside the solenoid the magnetic field is zero therefore the flux through the rest of the loop's area is zero. That makes sense, no?
That makes complete sense! I forgot about it. Thanks!
 

FAQ: Faraday's law -- Confusion about which Area to use in calculations

What is Faraday's Law of Electromagnetic Induction?

Faraday's Law of Electromagnetic Induction states that the induced electromotive force (EMF) in a closed circuit is directly proportional to the rate of change of magnetic flux through the circuit. Mathematically, it is often expressed as EMF = -dΦ/dt, where Φ is the magnetic flux.

How do you determine the area to use in Faraday's Law calculations?

The area to be used in Faraday's Law calculations is the area through which the magnetic field lines pass and that is bounded by the closed conducting loop. This area is perpendicular to the magnetic field lines. If the loop is not flat or the field is not uniform, you may need to integrate over the surface to find the total flux.

Does the orientation of the area affect the calculation of magnetic flux?

Yes, the orientation of the area relative to the magnetic field lines significantly affects the calculation of magnetic flux. The magnetic flux is given by Φ = B * A * cos(θ), where B is the magnetic field strength, A is the area, and θ is the angle between the magnetic field lines and the normal (perpendicular) to the area. If the area is not perpendicular to the magnetic field, you need to account for this angle.

What happens if the shape of the loop changes during the induction process?

If the shape of the loop changes during the induction process, the area through which the magnetic flux is calculated also changes. This change in area must be taken into account when calculating the rate of change of magnetic flux. The induced EMF will depend on how quickly the area changes as well as how the magnetic field changes.

Can Faraday's Law be applied to non-uniform magnetic fields?

Yes, Faraday's Law can be applied to non-uniform magnetic fields. In such cases, the magnetic flux must be calculated by integrating the magnetic field over the entire area of the loop. This involves breaking down the area into infinitesimally small elements, calculating the flux through each element, and then summing these contributions to find the total magnetic flux.

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