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

• uterii
In summary, 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. Magnetic fields and electric fields (I think. I'm not sure what else was involved) were involved. The current in the second coil was found to be 0.1mA when the voltage in the first coil was constant, but there was no induced current when the voltage was linearly increased over 10sec. The induced voltage was found to be 3.464*〖10〗^(-5) Wb when the power in the first coil was increased linearly.
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.

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 ?

BvU said:
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

Last edited:
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.

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.

## 1. Why are my calculations in the Faraday Lenz lab not accurate?

There could be multiple reasons why your calculations are not accurate. Some common reasons include errors in experimental setup, incorrect measurements, and using incorrect formulas. It is important to carefully double-check all your inputs and calculations to identify and correct any mistakes.

## 2. How can I improve my calculations in the Faraday Lenz lab?

To improve your calculations, make sure you are using accurate measurements and following the correct formulas. Additionally, you can try repeating the experiment multiple times and taking an average of your results to minimize any errors. It is also helpful to seek guidance from a teacher or mentor if you are still struggling with your calculations.

## 3. What is the Faraday Lenz law and how does it relate to my calculations?

The Faraday Lenz law states that the induced electromotive force (EMF) in a closed loop is equal to the rate of change of magnetic flux through that loop. This law is important in understanding the relationship between magnetic fields and electrical currents, and it can be used to calculate the induced EMF in a given setup.

## 4. How does the Faraday Lenz lab relate to real-world applications?

The Faraday Lenz lab demonstrates the principles of electromagnetic induction, which is a fundamental concept in modern technology. This law is used in various real-world applications such as generators, transformers, and electric motors. Understanding these principles can help us design and improve these technologies.

## 5. What can I do if my calculations are still not making sense?

If you are still having trouble with your calculations, it may be helpful to revisit the theory and concepts behind the experiment. You can also consult with classmates or your instructor for additional clarification. It is important to have a strong understanding of the principles before attempting to make calculations.

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