What is the current induced in a wire loop placed in a changing magnetic field?

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Homework Help Overview

The problem involves a closed wire loop placed in a changing magnetic field, specifically examining the induced current in the loop due to an increasing magnetic field. The loop is described as having a square shape with a given side length and resistance, and participants are asked to explore the relationship between the induced current and the magnetic field direction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply formulas related to electromotive force (E) and current (I) but questions the validity of their approach. Some participants suggest reconsidering the formulas used, particularly questioning the relevance of velocity in the context of the problem.

Discussion Status

Participants are actively discussing the application of Faraday's law of induction and exploring the correct approach to calculate the induced voltage. There is a recognition of the need to clarify the variables involved and the appropriateness of the formulas being used. Guidance has been offered regarding the correct law to apply, but no consensus has been reached on the final calculations.

Contextual Notes

Participants note the lack of information regarding velocity and discuss the implications of using different formulas in the context of the problem. There is also mention of the loop's negligible inductance, which may influence the discussion of induced current.

moenste
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Homework Statement


A closed wire loop in the form of a square of side 4 cm is placed with its plane perpendicular to a uniform magnetic field, which is increasing at the rate of 0.3 T s-1. The loop has negligible inductance, and a resistance of 2 * 10-3 Ω. Calculate the current induced in the loop, and explain with the aid of a clear diagram the relation between the diraction of the induced current and the direction of the magnetic field.

Answer: 0.24 A.

2. The attempt at a solution
Well, I used the E = B L v and I = V / R formulas.

E = 0.3 * (4 / 100) = 0.012 V.

I = 0.012 / (2 * 10-3) = 6 A.

What's wrong here?
 
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Hi!

Here's a hint -
moenste said:
E = B L v
Does this formula seem to apply here? Could you please list the value of each of these variables?
 
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LemmeThink said:
Hi!

Here's a hint -

Does this formula seem to apply here? Could you please list the value of each of these variables?
Hi!

E = voltage, B = magnetic field, L = length, v = velocity.

If know that this formula is not the best fit for this problem (we don't know velocity). But which one do you suggest?
 
Do you know Faraday's law of induction?
 
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LemmeThink said:
Do you know Faraday's law of induction?
Got it from here. Thank you!

E = - N (d Φ / d t)

d Φ / d t = 0.3 T s-1 * A, where A = (4 / 100) * (4 / 100) = 1.6 * 10-3 m2.

E= - 1 * 0.3 * 1.6 * 10-3 = - 4.8 * 10-4 V.

I = V / R = 4.8 * 10-4 / 2 * 10-3 = 0.24 A.
 
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