Magnetic flux of magnetic field changing as a function of time

In summary, the conversation discusses finding the flux and current in a bar with a changing magnetic field. The individual is unsure if their approach is correct and asks for guidance. The key piece of information is that the bar is moving at a constant velocity, which must be taken into account when finding the current.
  • #1
besebenomo
11
1
Homework Statement
There is a circuit with resistance R, a moving bar of lenght l moves at constant velocity v=l/T and at t=0 the bar is in position x=0. In the beginning the circuit is in a region where B=0, the the bar starts moving into a region with a non-zero magnetic field (see figure), which varies with time.

What is the current flowing in the circuit?
Relevant Equations
Magnetic flux, Faraday's law
$$B(t) = B_{0} \frac{t^2}{T^2}$$

for ##0 \leq t \leq T##

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The issue here is more conceptual, because once I find the flux of B I know how to proceed to find the current. I got velocity (but it seems to me that it is the initial velocity), I could use it to find the time in function of space, but not sure if that is correct...

Instead I tried this way:
$$\Phi(B) = B_{0}\frac{t^2}{T^2} x(t)l$$
Should I integrate instead? And change variable?
 
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  • #4
besebenomo said:
The issue here is more conceptual, because once I find the flux of B I know how to proceed to find the current. I got velocity (but it seems to me that it is the initial velocity), I could use it to find the time in function of space, but not sure if that is correct...

Instead I tried this way:
$$\Phi(B) = B_{0}\frac{t^2}{T^2} x(t)l$$
Should I integrate instead? And change variable?
You have the flux and it is what you say. Since you say you know how to proceed to find the current, do it and show your work. One piece of information you need to bring into the picture is that the bar is moving at constant velocity. What does that mean? Hint: You need to write Newton's second law just like in the other thread.
 
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FAQ: Magnetic flux of magnetic field changing as a function of time

1. What is magnetic flux?

Magnetic flux is a measure of the amount of magnetic field passing through a given surface. It is represented by the symbol Φ and is measured in units of webers (Wb).

2. How does magnetic flux change as a function of time?

Magnetic flux can change as a function of time if there is a changing magnetic field passing through a surface. This can occur if the strength or direction of the magnetic field changes, or if the surface itself moves in relation to the field.

3. What factors affect the change in magnetic flux over time?

The change in magnetic flux over time can be affected by the strength and direction of the magnetic field, the size and orientation of the surface, and the speed and direction of movement between the surface and the field.

4. How is the change in magnetic flux measured?

The change in magnetic flux can be measured using a device called a fluxmeter, which calculates the change in magnetic flux by detecting the induced voltage in a coil of wire placed in the changing magnetic field.

5. What are some real-world applications of understanding the change in magnetic flux over time?

Understanding the change in magnetic flux over time is important in many fields, including electrical engineering, physics, and geophysics. It is used in the design of motors and generators, as well as in studying the Earth's magnetic field and its effects on our planet.

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