Induced magnetic flux through a coil

In summary, the problem involves a circular conducting coil with 100 turns and a time-varying external magnetic flux density applied along the z-axis. The total magnetic flux through the coil as a function of time can be calculated using the formula Φt = Φb - Φi, where Φt is the total magnetic flux, Φb is the externally applied magnetic flux, and Φi is the flux induced by Lenz's law. To determine Φi, the formula for B must be used, B = Bi(1 - 3(t/ti)^2 + (t/ti)^3), and then the induced EMF can be calculated using E = -N(dΦ/dt).
  • #1
Gnarlywhale
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Homework Statement


A circular conducting coil with N=100 turns and radius "r" is oriented in the xy plane. The leads of the coil are connected to a circuit with resistance "R." A time varying external magnetic flux density "B" is applied along the z-axis.

What is the total magnetic flux through the coil as a function of time?

Homework Equations


Φ = BA

The Attempt at a Solution


Φt = Φb - Φi
Φt = BA - Φi

(where Φt is the total magnetic flux through the coil, Φb is the externally applied magnetic flux and Φi is flux induced by lenz's law).

I am aware that there is an induced magnetic flux but cannot figure out how to determine it from the external magnetic flux. Is there just some equation I can't seem to locate?
 
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  • #2
Are you sure that's the whole problem? You can't determine the induced magnetic flux unless you know how B varies with time, because induced EMF is equal to negative the change the magnetic flux.
 
  • #3
They do give you a formula for B,

B = Bi(1 - 3(t/ti)^2 + (t/ti)^3)

Everything is still left as a variable.

So from this then, E = -N(dΦ/dt) = -100*Bi(1 - 3(t/ti)^2 + (t/ti)^3) ?

And then how do I get flux from this emf?
 
Last edited:

1. What is induced magnetic flux through a coil?

Induced magnetic flux through a coil is the phenomenon where a changing magnetic field creates an electric current in a nearby coil. This is known as electromagnetic induction and is the basis for many important technologies, such as generators and transformers.

2. How is induced magnetic flux through a coil calculated?

The induced magnetic flux through a coil can be calculated using Faraday's law of electromagnetic induction, which states that the magnitude of the induced electromotive force (EMF) is equal to the rate of change of magnetic flux through the coil. This can be expressed as: EMF = -N * dΦ/dt, where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux.

3. What factors affect the magnitude of induced magnetic flux through a coil?

The magnitude of induced magnetic flux through a coil is affected by several factors, including the strength and rate of change of the magnetic field, the number of turns in the coil, and the material and shape of the core inside the coil.

4. What is the difference between induced magnetic flux and permanent magnetic flux?

Induced magnetic flux is temporary and only occurs when there is a changing magnetic field, while permanent magnetic flux is constant and does not require a changing magnetic field. Permanent magnetic flux is typically created by permanent magnets, while induced magnetic flux is created by electric currents.

5. What are some real-world applications of induced magnetic flux through a coil?

Induced magnetic flux through a coil is used in many technologies, such as generators, transformers, and electric motors. It is also utilized in wireless charging, electromagnetic levitation, and magnetic sensors. Additionally, electromagnetic induction has important applications in the field of electromagnetics and communications.

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