Faraday Lenz lab - My calculations are Way off and I'm not sure why

[uterii]

The purpose of the lab was to measure, and also calculate, the induced current in a disconnected coil, due to a second coil connected to a power supply. Involved magnetic fields and electric fields (I think.



For the purposes of this lab, the magnetic permittivity is 1.26*10-6, the number of turns is 500, and the radius of the coil is 10.5cm.

B=N (μ_0 I)/2R
ϕ=B∙A
=N*(u0*I)/2 * R2 /(R2 +x2 )3/2



Magnetic Field Created by the First Coil
I_left=18Ω/18V=1 Amp
B_left=500*((1.26*〖10〗^(-6) )*1Amp)/2*(.105m)^2/〖〖〖((.105m)〗^2+(.105m)〗^2)〗^(3/2) = 0.0010 Tesla
Current in Second Coil when Voltage in First Coil is Constant
In this situation, there is no induced current in the second loop. For an induced current to exist, there must be a change in flux over time. This is impossible when current is held constant.
Current in Second Coil when Voltage Linearly Increased over 10sec
ϕ_initial=0 Wb
ϕ_final= 0.0010 Tesla*(π*(10.5cm)^2 )=3.464*〖10〗^(-5) Wb
ε=-((3.464*〖10〗^(-5) Wb-0 Wb))/10s=3.46*〖10〗^(-6) V
I_induced=18Ω/(3.46*〖10〗^(-6) V)=5196896 Amp


My TA has told us that the induced current should be calculated as ~0.1mA, and experimentally the induced current was found to be 0.6mA. Obviously I am WAY off, but I'm honestly not sure what I'm doing wrong.

 

[BvU]

I_induced=18Ω/(3.46*〖10〗^(-6) V)=5196896 Amp is weird. Wasn't Ohms law a little different ?

Any measurement results for the induced voltage ?
I must say I find a change of 1 A in 10s rather slow, so maybe these low values can be expected.
I do find the ##\Phi_{\rm final}## value you found rather low. Can you check ?

Is there a drawing of the setup ? How far apart are the two coils ? Orientation ?

 

[uterii]

I_induced=18Ω/(3.46*〖10〗^(-6) V)=5196896 Amp is weird. Wasn't Ohms law a little different ?

Any measurement results for the induced voltage ?
I must say I find a change of 1 A in 10s rather slow, so maybe these low values can be expected.
I do find the ##\Phi_{\rm final}## value you found rather low. Can you check ?

Is there a drawing of the setup ? How far apart are the two coils ? Orientation ?

The two coils are 10.5cm apart, and they are parallel to one another. Each has a radius of 10.5cm, and the resistance of each coil is 18Ω.

We did not measure the induced voltage, just the induced current.

Ohm's law is V=IR. Ah, I see a mistake! So that was part of my problem, but something before that step is still off.

I've checked my calculation of ##\Phi_{\rm final}##, and I'm getting the same answer, so I'm worried it is an algebra error.

When inducing a current into the second coil, we had the power source increase linearly from 0V to 18V in 10seconds

 

[BvU]

Good. Now I use your first formula and get B=N (μ_0 I)/(2R) and get 0.003 T.

What do you do to get ##\Phi## ?

Do you now see why the rules and guidelines force using the template ? Saves time, yours and ours... Gets you better help too.

 

[HalfLostAndSearching]

It seems like there may be some errors in your calculations. It would be helpful to review the equations and make sure you are using the correct units and values for each variable. Additionally, double-check your calculations to ensure there are no mistakes. It is also important to consider any potential sources of error in the experiment itself, such as imperfect equipment or external magnetic fields.

One possible reason for the discrepancy between your calculated and experimental results could be the assumption that the magnetic permeability (μ) is equal to 1.26*10^-6. This value is typically used for free space, but in a lab setting, the permeability of the material surrounding the coils (such as air or a non-magnetic material) may be slightly different. This could affect the strength of the magnetic field and therefore the induced current.

Another factor to consider is the direction of the induced current. The Lenz's law states that the direction of the induced current will oppose the change in magnetic flux. So, depending on the direction of the changing magnetic field, the induced current may flow in the opposite direction of what you have calculated. It is important to carefully consider the signs and directions of all variables in your equations.

In addition, it may be helpful to discuss your calculations and results with your TA or other students in the class. Collaborating and discussing different approaches can often lead to a better understanding and identification of any errors.

Overall, it is important to carefully review your calculations and consider any potential sources of error in the experiment. With further analysis and discussion, you should be able to identify the reasons for the discrepancy and make any necessary adjustments to your calculations.