Faraday's law and Magnetic Fields

[maksym_slnc]

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

$$
\varepsilon=\oint \overrightarrow{\mathbf{E}} \cdot d \overrightarrow{\mathbf{l}}=-\frac{d \Phi_{\mathrm{m}}}{d t} .
$$
${\mathbf{B}}=\frac{\mu_0 I \hat{\mathbf{j}}}{2 \pi\left(y^2+R^2\right)^{3 / 2}}$

I am not really sure which direction i am moving in with this solution

 

[TSny]

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.

 

[maksym_slnc]

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.

 

[TSny]

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.