Potential difference across a solenoid

[Angelos]

Hi,

I have just started studying EM induction and I got stuck with the derivation of potential difference across a solenoid when the current in it is changing. My textbook (Physics for Scientists and Engineers by Tipler) derives it in very mathematical way just by saying that because the induced EMF in solenoid is equall to -L*dI/dt and the decrease in potential due to the resistance of the solenoid is -Ir the totel potential difference is -L*dI/dt - Ir. However I would prefere using the Lenz's Law for deriving the direction of induced EMF. So I say that because the current is in some direction it causes a decrease in potential in that direction due to the resistance. That is -Ir. But because the induced current wants to oppose the original current, the induced EMF and the potential difference due to resistance would have opposite signs. That means that the total potential difference across a solenoid would be abs(LdI/dt - Ir). Where have I made a mistake? Thanks for your help.

 

[mukundpa]

... But because the induced current wants to oppose the original current, the induced EMF and the potential difference due to resistance would have opposite signs.

What about induced current when the current in solenoid is decreasing? Will it still oppose the origional current?

I think potential difference and EMF are different terms and you must understand them clearly. What do you think about the direction of current and potential difference within an electric cell?

 

[Angelos]

What about induced current when the current in solenoid is decreasing? Will it still oppose the origional current?

I think potential difference and EMF are different terms and you must understand them clearly. What do you think about the direction of current and potential difference within an electric cell?

Well I didn't really think of the situation when the current is decreasing. In that case the induced current would be in the direction of the current. However isn't it true that when I have a circuit with a power supply, switch and a solenoid and I turn the switch on, the current starts from zero and keeps increasing until some value? Or does it first go up and then down again? But in that case we would have to use that equation I wrote for the part, where it goes up...

Yes, EMF and potential difference are different terms. I think of EMF as a part of the total potential difference. The example you wrote is a good one. The current in a battery goes from lower potential to higher potential. So it opposes the EMF and thus the total potential difference is the EMF - Ir, where r is the internal resistance.