Induced Current in Square Loop

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Homework Help Overview

The discussion revolves around a problem involving a square loop with a given resistance and a time-varying magnetic field. Participants are exploring how to calculate the induced current in the loop at specific times based on Faraday's law of electromagnetic induction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Some participants attempt to apply Faraday's law to find the induced voltage and subsequently the current. There is a question about the initial conditions and the implications of the magnetic field at t=0.0s.

Discussion Status

Participants are actively discussing the application of Faraday's law, with some confirming the approach of using voltage derived from the rate of change of the magnetic field. There is ongoing exploration of the implications of the magnetic field's behavior over time.

Contextual Notes

The problem includes specific values for resistance and dimensions of the loop, as well as a time-dependent magnetic field equation. There is an indication that assumptions about the magnetic field at certain times are being questioned.

qlzlahs
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Homework Statement


A 21cm×21cm square loop has a resistance of 0.12 Ω . A magnetic field perpendicular to the loop is B=4t−2t^2, where B is in tesla and t is in seconds.
(A) What is the current in the loop at t=0.0s?
(B) What is the current in the loop at t=1.0s?

Homework Equations


for a square loop, B = (√2)(μ_0*I)/(π*R), where R is the length of the side

The Attempt at a Solution


(A) I assumed that at t = 0, B = 4(0) - 2(0^2) = 0.
0 = (√2)(μ_0*I)/(π*.21), but that means I = 0 A and that didn't work.
Help please? Thanks.
 
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You must use Faraday's law of electromagnetic induction.
 
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cnh1995 said:
You must use Faraday's law of electromagnetic induction.

So I use V = -A*(dB/dt), then use V = IR to find the current?
 
qlzlahs said:
So I use V = -A*(dB/dt), then use V = IR to find the current?
Correct..
 
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