Relationship between potential and induced emf?

[Yoriko]

Homework Statement

[PLAIN]http://img220.imageshack.us/img220/2589/44045733.png

Semicircular wire MN of diameter L moves with speed v perpendicularly through a uniform magnetic field of strength B.

1. Find the magnitude of the induced emf generated between M and N.
2. State whether M or N is at a higher potential.

Homework Equations

E = BLv

The Attempt at a Solution

1. Given answer: Induced emf = BLv

However, I was wondering if you can use that equation even if it's not a closed circuit?
In the semicircular wire, there shouldn't be magnetic flux linkage. And even if there was, there is no change in magnetic flux linkage.

2. N is at a higher potential

There is opposing force that resists the motion of the wire ( is this reason correct?), which, by Fleming's left hand rule, results in an induced current (if the circuit were to be closed) flowing from M to N. Thus, N is at higher potential as a result of the induced "current".

However, I know that current flows from higher potential to lower potential. So is it right to say that in the case of an induced current, if it flows from M to N, N is at a higher potential?

 

[Quinzio]

However, I was wondering if you can use that equation even if it's not a closed circuit?

Sure, you can, you have to.
Just be careful what "length" is.

If it was a closed circuit of zero resistance, there would be no voltage at all.
V=RI, R=0, so V=0 (for closed loops of zero resistance)

However, I know that current flows from higher potential to lower potential. So is it right to say that in the case of an induced current, if it flows from M to N, N is at a higher potential?

Pay attention to the charge sign.

There is opposing force that resists the motion of the wire

No there's no opposing force.

 

[Yoriko]

No there's no opposing force.

Then how is there an induced emf?

[PLAIN]http://img207.imageshack.us/img207/5853/93128344.png

Do you take "Force" to be in direction of the velocity?

 

[alkmini]

i know the thread is old but i have a question
what shall we take as a length to calculate E, the length πr of the arc or the length 2r of the line segment and why?
thanks a lot

 

[asteriatic]

I would like to clarify that the relationship between potential and induced emf is not as straightforward as it may seem. The equation E = BLv is valid for a closed circuit, where the induced emf is equal to the rate of change of magnetic flux linkage. In the case of a semicircular wire moving through a magnetic field, there is no closed circuit and thus the concept of magnetic flux linkage does not apply. Therefore, the equation E = BLv cannot be directly applied in this scenario.

However, in this case, the induced emf can still be calculated using the equation E = BLv, if we consider the two ends of the semicircular wire (M and N) as the two ends of a hypothetical closed circuit. In this case, the induced emf between M and N would be equal to the rate of change of magnetic flux linkage between these two points.

Regarding the question of which end (M or N) is at a higher potential, it is important to note that potential is a relative quantity and can only be compared between two points. In this case, the potential difference between M and N would depend on the direction of the induced current (if the circuit were to be closed) and the direction of the magnetic field. If the induced current is flowing from M to N, then N would be at a higher potential compared to M. However, if the induced current is flowing from N to M, then M would be at a higher potential compared to N.

In summary, the relationship between potential and induced emf is complex and depends on various factors such as the direction of the induced current and the direction of the magnetic field. It is important to carefully consider these factors when analyzing the potential and induced emf in a system.