Induced current from changing magnetic field

In summary, the conversation discusses how to calculate the total flux through a loop using the equations emf = - d(Ф)/dt and Ф = B (dot) A. It is mentioned that B is a function of R and that the total flux will be a function of i. The only changing variable with time is i, while A and R are constant.
  • #1
iharuyuki
16
1

Homework Statement


upload_2015-4-15_10-54-23.png


Homework Equations


emf = i (induced) R
emf = - d(Ф)/dt
Ф = B (dot) A
B = μi/(4piR)

The Attempt at a Solution



emf = - d(Ф)/dt
emf = - d( B (dot) A )/dt
emf = - d[ (μi/(4piR) * A ]/dt, A and B are perpendicular


Really not sure how to proceed from here as there are multiple derivatives (di/dt dR/dt and dA/dt) that I don't quite get.

Thank you very much.
 
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  • #2
You have to calculate the total flux φ through the loop. Since B is a function of R, you have to integrate to find the total flux, which will be a function of i. In terms of your question about time derivatives, the only thing changing with time is i. A and R are constant in time.
 
  • #3
Got it! Thank you very much.
 

1. What is induced current from changing magnetic field?

Induced current from changing magnetic field, also known as electromagnetic induction, refers to the production of an electric current in a conductor when it is exposed to a changing magnetic field. This phenomenon was first discovered by Michael Faraday in the 1830s.

2. How is induced current from changing magnetic field generated?

Induced current from changing magnetic field is generated when a conductor, such as a wire, is moved through a magnetic field or when the strength of the magnetic field changes. This movement or change in magnetic field creates a force that causes electrons to flow in the conductor, producing an electric current.

3. What factors affect the strength of induced current from changing magnetic field?

The strength of the induced current from changing magnetic field depends on several factors, including the strength of the magnetic field, the speed of the movement of the conductor, the angle at which the conductor cuts through the magnetic field, and the number of turns in the conductor.

4. What are the applications of induced current from changing magnetic field?

Induced current from changing magnetic field has various applications in our daily lives, including power generation, electric motors, transformers, and generators. It also plays a crucial role in technologies such as wireless charging, magnetic levitation, and magnetic resonance imaging (MRI).

5. How does Lenz's law explain induced current from changing magnetic field?

Lenz's law states that the direction of the induced current in a conductor will always be in such a way that it opposes the change in magnetic flux that caused it. This law helps to explain the direction of the induced current and why it flows in a particular direction in relation to the changing magnetic field.

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