Voltage induced by changing field

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SUMMARY

The discussion focuses on calculating the induced voltage and current in a 30-turn wire loop with a diameter of 14 cm and a resistance of 4 ohms, subjected to a varying magnetic field described by the equation B(t) = 4t^3 - 9t^2 + 3t - 28. At t = 2 seconds, the induced voltage across the loop can be determined using Faraday's Law of Electromagnetic Induction. The current in the loop is calculated using Ohm's Law, and the direction of the induced current can be explained using Lenz's Law, which states that the induced current will oppose the change in magnetic flux through the loop.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Knowledge of Ohm's Law and electrical resistance
  • Familiarity with Lenz's Law and magnetic flux concepts
  • Basic calculus for evaluating the magnetic field function B(t)
NEXT STEPS
  • Calculate induced voltage using Faraday's Law for different time intervals
  • Explore the relationship between magnetic flux and induced current
  • Learn about the applications of Lenz's Law in real-world scenarios
  • Investigate the effects of varying magnetic fields on different loop configurations
USEFUL FOR

Physics students, electrical engineers, and anyone interested in understanding electromagnetic induction and its practical applications in circuits.

Cyan Ray
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5. A wire is formed into a 30 turn loop whose diameter is 14 cm and the resistance of the loop is 4 ohmns. The loop is placed on this page and a magnetic is going directly into the plane of the paper and is varying according to the formula
B(t) = 4t^3 - 9t^2 + 3t - 28

Part (a): What is the voltage across the loop at t = 2s?
Part (b): What is the current in the loop at this time?
Part (c): What is the direction of the induced current? Explain
Here is my solution
 

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Is this right?

And as for c) I have no explanation...what is an approriate explanation?
 
Cyan Ray said:
And as for c) I have no explanation...what is an approriate explanation?
Is the flux increasing or decreasing at t = 2s? :smile:
 

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