Faraday's law and Magnetic Fields

AI Thread Summary
The discussion focuses on correcting a formula related to Faraday's law and magnetic fields, emphasizing the need for proper dimensions on the right-hand side of the equation. Participants noted that the formula should simplify to the magnetic field at the center of a circular current loop when x equals zero. There was a clarification regarding the vector form of the expression, which initially lacked the appropriate unit vector notation. After adjustments were made, it was suggested that a reasonable answer should now be achievable. The conversation highlights the importance of precision in mathematical expressions related to electromagnetic theory.
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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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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