Inductance and solenoid question

[kervyn]

Homework Statement

I am designing a solenoid for a project to meet several specifications. I am attempting to induce an emf of approximately 2V in my circuit by moving a magnet in and out of the coil. I know the magnet has an approximate field strength of 1T. I am trying to determine necessary solenoid specs (#of wraps, length, radius) based on these values to generate the emf.

However i am unsure how to calculate values such as change of flux over time and change of current over time needed to determine necessary coil characteristics.

Homework Equations

Faraday's Law of induction

ε = -dΦ/dt

Induction

L = μN^2A/L

Self Induced Emf

ε = -Ldi/dtCould the change of flux with respect to time depend based on how fast the magnet is moved in and out of the coil?

Appreciate any insight!

 

[rude man]

Could the change of flux with respect to time depend based on how fast the magnet is moved in and out of the coil?

Yes. That's what emf = -N d(phi)/dt says. Phi = B x area of coil. That goes for every winding in your solenoid. The total emf is the sum of the emf's for each winding since the windings are all in series. You will have to determine dB/dt for every winding. B is the field for a winding and dB/dt is how rapidly you're changing B by moving the magnet in & out of that winding. How were you thinking of moving the magnet?

 

[kervyn]

Yes. That's what emf = -N d(phi)/dt says. Phi = B x area of coil. That goes for every winding in your solenoid. The total emf is the sum of the emf's for each winding since the windings are all in series. You will have to determine dB/dt for every winding. B is the field for a winding and dB/dt is how rapidly you're changing B by moving the magnet in & out of that winding. How were you thinking of moving the magnet?

Thanks for the response. The magnet will be attached to a spring loaded platform moving down and up. The spring constant is quite high so the magnet should move at a decent speed

 

[rude man]

OK. You can hope for a very approximate estimate of your emf with the magnet bobbing in & out, including magnitude and waveform shape. Don't expect a nice sinusoid! :-)

 

[rezeew]

I would suggest starting by rearranging the equation for Faraday's Law of induction to solve for the change in flux over time, as it is the main factor in determining the induced emf. This can be done by dividing both sides by -dΦ/dt and then integrating with respect to time. This will give you a relationship between the change in flux and the induced emf.

Next, you can use the equation for inductance to determine the necessary number of wraps, length, and radius of the solenoid. This equation takes into account the permeability of the material, the number of wraps, the cross-sectional area, and the length of the solenoid. To determine the necessary parameters, you will need to rearrange the equation and plug in the known values for the magnet's field strength, the desired induced emf, and the material being used for the solenoid.

The change of current over time, or the rate of change of current, can also be calculated using the equation for self-induced emf. This equation takes into account the inductance, the change in current, and the change in time. By rearranging the equation, you can solve for the change in current over time and use this to determine the necessary parameters for the solenoid.

Finally, it is important to note that the change of flux with respect to time can indeed be affected by the speed at which the magnet is moved in and out of the coil. The faster the movement, the greater the change in flux and therefore the greater the induced emf. However, this also depends on the other factors such as the inductance and the material used for the solenoid.

Overall, it is important to carefully consider all the equations and factors involved in determining the necessary solenoid specs. Any additional insight or assistance from a physics expert or a colleague with experience in designing solenoids could also be helpful in ensuring accurate and efficient results.