Calculating Induced EMF in a Coil

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SUMMARY

The discussion focuses on calculating the induced electromotive force (emf) in a 32-turn circular coil with a radius of 4.60 cm and a resistance of 1.00 ohms, placed in a time-varying magnetic field described by the equation B = 0.0100t + 0.0400t². The induced emf is calculated using the formula Emf = -d/dt(NABcosθ), leading to a result of -97.4 mV at t = 5.60 seconds. The user expresses uncertainty regarding the impact of resistance on the final answer, indicating a need for clarification on the relationship between induced emf and resistance.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Familiarity with the concepts of magnetic flux and induced emf
  • Basic knowledge of calculus, specifically differentiation
  • Ability to perform calculations involving circular coils and magnetic fields
NEXT STEPS
  • Review the principles of Faraday's Law and its applications in electromagnetic induction
  • Learn about the effects of resistance on induced emf in circuits
  • Explore the relationship between magnetic field strength and induced voltage in coils
  • Study practical examples of induced emf calculations in various coil configurations
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in the practical applications of electromagnetic induction in coils and circuits.

Ithryndil
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Homework Statement


A 32 turn circular coil of radius 4.60 cm and resistance 1.00 is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.0100t + 0.0400t2, where t is in seconds and B is in teslas. Calculate the magnitude of the induced emf in the coil at t = 5.60 s.

Homework Equations


Emf = -d/dt(NABcos\theta)

The Attempt at a Solution



I pulled out the -NAcos(theta) as a constant

-NAcos(theta)d/dt(B)
-NAcos(0)d/dt(0.0100t+0.0400t^2)
-NA(0.0100+0.0800t) where t = 5.6, N = 32 and A = pi*(0.046^2)

The answer I got was: -97.4 mV. I have one submission left and am not sure if that's right considering there is a resistance.
 
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