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

[e.pramudita]

Homework Statement

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

 

[Andrew Mason]

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?

This is a Faraday's law problem. State Faraday's law.

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

 

[Andrew Mason]

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