The Right Hand Rule: Direction of Ring Induced Current in Solenoid

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When a metal ring is placed near a solenoid, the direction of the induced current depends on the state of the solenoid's circuit. Initially, when the switch is closed, the induced current in the ring flows counter-clockwise to oppose the solenoid's clockwise current, as per Lenz's law. After several seconds of the switch being closed, the induced current ceases because there is no longer a change in magnetic flux. When the switch is opened, the current in the ring adjusts to maintain the magnetic state, transitioning from counter-clockwise to clockwise as the solenoid's current decreases. Understanding the right hand rule and Lenz's law is crucial for determining these current directions.
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If a metal ring is places near a solenoid, what is the direction of the induced current in the ring for the following cases

a. At the instant the swithc in the circuit containing the solenoid is thrown closed.

b. After the switch has been closed for several seconds.

c. At the instant the switch is thrown open.

I think that I have to do the right hand rule for this problem, but my problem is that I have a hard time understanding the right hand rule, so is there any way of finding the direction for something other than the right hand rule? How about the dot product? For instance, what does "into the page" and "out of the page" mean?
 
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this looks like a Lenz's law problem. Basically you have zero current to begin with. Lenz's law states that the induced current in a object will be in a direction so that the initial state of current is maintained. Kinda like angular momentum. So if I have zero current to begin with, then the instant after I throw the swtich the direction of the current will oppose that of the solenoid. So if the current flows clockwise in the solenoid, it will flow counter-clockwise in the ring. When the solenoid is turned off, then as the clockwise current in the solenoid approaches zero, the current in the ring will become less counter-clockwise and will want to tend towards a clockwise direction.
 
For the case where the switch has been closed for "several seconds," why is the mention of those "several seconds" so important to the problem?
 
For the case where the switch has been closed for "several seconds," why is the mention of those "several seconds" so important to the problem?

because as the switch is intially turned on the change in magetic flux causes the induced current. but once the switch has been turned on for several second the induced current will be no longer because after those several second there is no more CHANGE in magnetic flux.

at least that what i think! :rolleyes:
 

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