How Does Lenz's Law Apply to EMF in a Triaxially Bent Wire?

In summary, the problem involves a wire bent into three circular segments with a radius of 9.2 cm each, forming a quadrant in the xy, yz, and zx planes. With a uniform magnetic field in the positive x direction, the magnitude of the EMF developed in the wire is calculated using Faraday's law and Lenz's law. The projected area for the flux is pi*r^2/4 and is multiplied by the given rate of change of the magnetic field. The components of the wire do not affect the EMF.
  • #1
ghetto_bird25
18
0

Homework Statement


A wire is bent into three circular segments each of radius r=9.2 cm. each segment is a quadrant of circle, ab lying in the xy plane, bc, in the yz plane, and ca lying in the zx plane. If a uniform magnetic field points in the positive x direction, what is in volts the magnitude of the emf developed in the wire when B increases at the rate of 3.4 mT/s?
http://edugen.wiley.com/edugen/courses/crs1141/art/images/c31/nw0500-n.gif


Homework Equations


so what i used was faraday's law and lenz's law by using the formula
[tex]\epsilon[/tex]=d(B A)/dt
and then since area (A) is constant you can bring it out. and area would equal 1/4[tex]\pi[/tex]r[tex]^{2}[/tex] and the dB/dt is given. the only problem is that i don't know what to do with the components as you have the pieces on all three axis and how wood i deal with each component?
 
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  • #2
There are no components for the EMF. Your projected area seems right.
Just multiply A and dB/dt.
 
  • #3
oh so jus do it for each section and add it up or make it 3/4pi*r^2 time dB/dt
 
  • #4
No. The projected area area for the flux is just the pi*r^2/4.
 
  • #5
oh ok thanks alot
 

FAQ: How Does Lenz's Law Apply to EMF in a Triaxially Bent Wire?

What is Lenz's Law?

Lenz's Law is a fundamental law of electromagnetism that states that the direction of an induced electromotive force (EMF) in a closed conducting loop will be such that it opposes the change that caused it.

How does Lenz's Law relate to electromagnetic induction?

Lenz's Law is a consequence of Faraday's Law of electromagnetic induction. It explains the direction of the induced EMF and its relationship to the changing magnetic field.

What is the significance of Lenz's Law in electrical circuits?

Lenz's Law plays a crucial role in understanding the behavior of electrical circuits. It helps predict the direction of the induced EMF and the resulting current flow in a circuit, which is essential for designing and troubleshooting electronic devices.

How does Lenz's Law apply to the movement of a conductor in a magnetic field?

When a conductor moves in a magnetic field, an EMF is induced in the conductor due to the changing magnetic flux. According to Lenz's Law, the direction of this induced EMF will be such that it opposes the motion of the conductor, resulting in a force called the Lenz's Law force.

Can Lenz's Law be violated?

No, Lenz's Law is a fundamental law of electromagnetism and has been extensively tested and verified through experiments. It is a fundamental principle that applies to all electromagnetic phenomena and cannot be violated.

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