How Fast Must a Magnetic Field Change to Induce a Specific Current?

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SUMMARY

The discussion centers on calculating the rate of change of a magnetic field required to induce a specific current in a conducting loop. Given a loop area of 7.4 x 10^-2 m², a resistance of 110 ohms, and a magnetic field strength of 0.18 T, the induced current target is 0.22 A. The relevant equations include magnetic flux (Φ = BA) and induced electromotive force (E = dΦ/dt), which can be combined with Ohm's Law (E = IR) to derive the necessary rate of change of the magnetic field in teslas per second (T/s).

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with the concepts of magnetic flux and induced EMF
  • Knowledge of Ohm's Law and its application in electrical circuits
  • Basic calculus for differentiating magnetic flux over time
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  • Study Faraday's Law of Electromagnetic Induction in detail
  • Learn how to calculate magnetic flux for different geometries
  • Explore applications of induced EMF in real-world electrical systems
  • Investigate the relationship between magnetic field strength and induced current in various materials
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Physics students, electrical engineers, and anyone interested in the principles of electromagnetic induction and its applications in circuit design.

triplezero24
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Ok, I need a lot of help on this one. A single conducting loop of wire has an area of 7.4*10^-2 m^2 and a resistance of 110 ohms. Perpendicular to the plane of the loop is a magnetic field of strength 0.18 T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.22 A?

So far all I can figure out is that Phi=BA. And I don't think that has anything to do with this problem.

Thanks for any and all help.
 
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Well, how do you relate the change in flux to the induced EMF? And once you have that, just use ohm's law to get the current.
 
you should know these formulae from your text

flux [tex]\Phi = \int B dA Cos \theta[/tex]
and induced emf [tex]E = \frac{d \Phi}{dt}[/tex]
and also the induced Emf is just live a voltage really so E = IR.

now try and rearrange these equatios to solve
 

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