Potential difference across a solenoid

• Angelos
In summary, the conversation discusses the derivation of potential difference across a solenoid when the current is changing. The textbook method uses mathematical equations, while the speaker suggests using Lenz's Law to determine the direction of induced EMF. There is also a discussion on the relationship between induced current, EMF, and potential difference. The conversation raises the question of what happens when the current in the solenoid is decreasing, and the speaker suggests that in that case, the induced current would be in the same direction as the original current. However, they also mention that the current may first increase and then decrease, in which case the equation for potential difference would need to be adjusted. The conversation concludes by stating that EMF and potential difference are
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.

Angelos said:
... 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?

mukundpa said:
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.

1. What is a solenoid?

A solenoid is an electrical coil that is typically wound in a helix shape. It is used to create a magnetic field when electric current is passed through it.

2. What is potential difference?

Potential difference, also known as voltage, is the difference in electrical potential between two points. It is measured in volts and represents the amount of energy needed to move a unit of electric charge from one point to another.

3. How is potential difference measured across a solenoid?

Potential difference across a solenoid can be measured using a voltmeter. The voltmeter is connected in parallel to the solenoid, allowing for the measurement of the potential difference between two points along the coil.

4. What factors affect potential difference across a solenoid?

The potential difference across a solenoid is affected by the number of turns in the coil, the strength of the magnetic field, and the current passing through the solenoid. It is also affected by the material and length of the wire used to make the coil.

5. What is the relationship between potential difference and current in a solenoid?

According to Ohm's Law, the potential difference across a solenoid is directly proportional to the current passing through it. This means that as the current increases, the potential difference across the solenoid also increases. Similarly, as the current decreases, the potential difference across the solenoid decreases.

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