Faraday's law and Magnetic Fields

In summary, the conversation was about checking a formula for the correct dimensions and numerical factors for magnetic field. The correct expression was found to be a vector form with an i hat.
  • #1
maksym_slnc
2
0
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
 
Physics news on Phys.org
  • #2
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:
  • #3
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
 
  • #4
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.
 

FAQ: Faraday's law and Magnetic Fields

What is Faraday's Law of Electromagnetic Induction?

Faraday's Law of Electromagnetic Induction states that a change in magnetic flux through a closed loop induces an electromotive force (EMF) in the wire that forms the loop. The induced EMF is directly proportional to the rate of change of the magnetic flux.

How is the magnetic flux calculated?

Magnetic flux (Φ) is calculated as the product of the magnetic field (B) and the area (A) it penetrates, and the cosine of the angle (θ) between the magnetic field and the normal to the surface. Mathematically, it is expressed as Φ = B * A * cos(θ).

What is Lenz's Law and how does it relate to Faraday's Law?

Lenz's Law states that the direction of the induced current (or EMF) will be such that it opposes the change in magnetic flux that produced it. This is a consequence of the conservation of energy and is incorporated into Faraday's Law to determine the direction of the induced EMF.

What are some practical applications of Faraday's Law?

Faraday's Law has numerous practical applications including the functioning of electrical transformers, electric generators, induction cooktops, and various types of sensors and inductors used in electronic circuits.

What is the difference between a magnetic field and magnetic flux?

A magnetic field (B) is a vector field that represents the magnetic influence on moving electric charges, electric currents, and magnetic materials. Magnetic flux (Φ), on the other hand, is a scalar quantity that measures the total magnetic field passing through a given area. While the magnetic field describes the strength and direction of magnetism, magnetic flux quantifies the amount of magnetic field passing through a surface.

Back
Top