Wire coil in decreasing magnetic field

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SUMMARY

A wire coil with a radius of 2 cm and 10 turns is subjected to a magnetic field that decreases from 2 T to 0 T over 10 ms. The coil is connected in series with a 5 Ω resistor. Using Faraday's law of induction, the induced electromotive force (EMF) can be calculated, leading to the determination of the current through the resistor. The magnetic flux is calculated using the formula Magnetic Flux = B⋅dA = Bπr², which is essential for finding the induced EMF as the magnetic field changes.

PREREQUISITES
  • Understanding of Faraday's law of induction
  • Knowledge of magnetic flux calculation
  • Familiarity with Ohm's law (V=IR)
  • Basic concepts of electromagnetism
NEXT STEPS
  • Study the application of Faraday's law of induction in various scenarios
  • Learn how to calculate induced EMF in changing magnetic fields
  • Explore the relationship between magnetic flux and current in circuits
  • Investigate the effects of resistance on induced current in coils
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in understanding the principles of induced current in wire coils within magnetic fields.

Pete Panopoulos
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Homework Statement


A wire coil of 2 cm with 10 turns is in a magnetic field of 2 T. The field is perpendicular to the plane of each turn of the coil. The coil is wired in series with resistor of 5 Ω. The field drops at a constant rate to 0.0 T in 10 ms. What is the current through the resistor?

Homework Equations


V=IR
Possibly F=ILxB ?
Magnetic Flux= B⋅dA = Bπr2

The Attempt at a Solution


I=V/R

We know that the magnetic field drops from 2T to 0T in .01 seconds, or -200T/s

and the Resistor is 5 Ω

Flux= B⋅dA = Bπ(.02)2

I'm assuming I'm missing a link to these things in my head any help would be appreciated
 
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Can you bring in Faraday's law of induction?
 

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