Faraday's law and Magnetic Fields

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Homework Help Overview

The discussion revolves around applying Faraday's law and understanding magnetic fields, particularly in the context of a formula related to the magnetic field at the center of a circular current loop.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants express uncertainty regarding the direction of their solutions and question the dimensional correctness of a formula related to magnetic fields. There are attempts to clarify the correct expression and its vector form.

Discussion Status

Some participants have provided guidance on checking the formula's dimensions and numerical factors, while others have acknowledged corrections to the expression being used. The conversation reflects a collaborative effort to refine understanding without reaching a definitive conclusion.

Contextual Notes

There is mention of specific conditions, such as the formula needing to reduce correctly for a particular case (##x = 0##) and the importance of vector notation in the expression.

maksym_slnc
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Homework Statement
A very large loop of metal wire with radius 1 meter is driven with a linearly increasing current at a rate of 200 amps/second . A very small metal wire loop with radius 5 cm is positioned a small distance away with its center on the same axis (the loops are coaxial). The small loop experiences an induced emf of 983nV . What is the separation of the loops in meters?
Relevant Equations
$$
\varepsilon=\oint \overrightarrow{\mathbf{E}} \cdot d \overrightarrow{\mathbf{l}}=-\frac{d \Phi_{\mathrm{m}}}{d t} .
$$
${\mathbf{B}}=\frac{\mu_0 I \hat{\mathbf{j}}}{2 \pi\left(y^2+R^2\right)^{3 / 2}}$
1682079672875.png

I am not really sure which direction i am moving in with this solution
 
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1682087140381.png
Check this formula. Note that that the right-hand side does not have the correct dimensions for magnetic field. Also, check the numerical factors in the equation. For ##x = 0## the formula should reduce to the field at the center of a circular current loop.

Otherwise, your approach looks correct.
 
Last edited:
TSny said:
Check this formula. Note that that the right-hand side does not have the correct dimensions for magnetic field. Also, check the numerical factors in the equation. For ##x = 0## the formula should reduce to the field at the center of a circular current loop.

Otherwise, your approach looks correct.
Oh, thanks a lot, it was a vector form, but without the i hat. Correct expression was this one.
correct expression.png
 
maksym_slnc said:
Oh, thanks a lot, it was a vector form, but without the i hat. Correct expression was this one.View attachment 325234
Ok. You should get a reasonable answer now.
 

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