Induced Current in Square Loop

AI Thread Summary
A square loop with a resistance of 0.12 Ω and dimensions of 21cm x 21cm is subject to a time-varying magnetic field described by B=4t−2t^2. At t=0.0s, the magnetic field is zero, leading to an initial current of 0 A, which is confirmed through calculations. To find the current at t=1.0s, Faraday's law of electromagnetic induction is applied, specifically using the equation V = -A*(dB/dt) and then V = IR to determine the current. The discussion emphasizes the correct application of these equations to solve for induced current in the loop. Understanding these principles is crucial for accurately determining the current at different time intervals.
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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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