Relationship of W and v in a region of uniform magnetic field

• e.pramudita
In summary, the attempt at a solution for this problem is to use Faraday's law and determine when current starts and stops being induced, calculate the rate of change of flux enclosed by the loop, and calculate the work done as a function of v.
e.pramudita

Homework Statement

https://dl.dropbox.com/u/63664351/Physics/Electromagnetic%20Induction.PNG

Homework Equations

W=mas.
Unknown relation between W v and B

The Attempt at a Solution

dW = m a ds = m dv/dt ds
dW/dv =m ds/dt = ma dv
So the gradient of graph W and v is positive. So it is linear.
But what role does magnetic field play in this case?

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e.pramudita said:

The Attempt at a Solution

dW = m a ds = m dv/dt ds
dW/dv =m ds/dt = ma dv
So the gradient of graph W and v is positive. So it is linear.
But what role does magnetic field play in this case?

How is work being done here? (hint: W = Force x distance. Is there a force here? What produces the force? What determines the magnitude of the force? What is the distance through which the force acts?) What effect does v have on the force? Does v affect the distance through which the force acts?

AM

Just to give you a bit of a feel for what is happening here, if a current is induced in the conducting loop as it moves through the magnetic field, that current will give rise to a magnetic field that opposes the motion. So to keep it moving at constant speed, a force would have to be provided to the loop in the direction of motion. That force is proportional to the induced current. The induced current is proportional to the induced emf, which is determined by Faraday's law.

The key to the exercise is to determine when a current starts being induced and when it ends and how it depends on v.

From Farday's law, the induced emf is proportional to the time rate of change of flux enclosed by the loop:

So to answer the problem, you must be able to answer these questions:

1. at what position of the loop in the field does the flux enclosed by the loop start to change? (ie. when current starts to flow and when a force is needed to maintain v).

2. at what position does the flux enclosed by the loop reach and remain at 0? (ie. when current stops and no force is needed to maintain v).

3. what is the rate of change of flux enclosed by the loop between positions 1. and 2.? Is it constant or does it vary? Describe the current that is induced. Since force is directly proportional to current, describe the force required to maintain v?

4. write out the expression for work as a function of v.AM

1. How are W and v related in a region of uniform magnetic field?

In a region of uniform magnetic field, W (the work done on a charged particle) and v (the velocity of the charged particle) are directly proportional. This means that as the velocity of the particle increases, the amount of work done on it also increases.

2. What is the formula for calculating the relationship between W and v in a region of uniform magnetic field?

The formula for calculating the relationship between W and v in a region of uniform magnetic field is W = qvBd, where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and d is the distance the particle travels in the field.

3. How does the direction of the magnetic field affect the relationship between W and v?

The direction of the magnetic field has no effect on the relationship between W and v. As long as the field is uniform, the relationship remains the same.

4. Is the relationship between W and v affected by the mass of the charged particle?

No, the relationship between W and v is not affected by the mass of the charged particle. This is because the formula for calculating W and v does not include the mass of the particle.

5. Can the relationship between W and v be applied to all types of charged particles?

Yes, the relationship between W and v can be applied to all types of charged particles, as long as they are moving in a region of uniform magnetic field. This includes electrons, protons, and other ions.

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