Inductive charging: Emf induced in two coil loops

In summary, the problem involves a charging station with two coils, one with N1 turns and area A1, and the other with N2 turns and area A2. The first coil is connected to a 120 VAC, 60 Hz source, while the second coil will fit completely inside the first. The questions ask for the EMF of both coils and the number of turns needed in the second coil to produce a 6 vac RMS source. The EMF of the base coil is not 0, as there is a changing flux induced by the AC current. The EMF of the device coil is found to be proportional to the base coil's EMF. Finally, the number of turns needed in the second coil can be
  • #1
khfrekek92
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0

Homework Statement


So I'm trying to figure out this problem:

The base of our charging station is composed of a coil with N1 turns and area A1 connected to a 120 VAC, 60 Hz source. The device has a smaller coil with N2 turns and area A2, which when attached will fit completely inside the charging coil.

A) What is the EMF of the base coil?

B) what is the EMF of the device coil?

C) how many turns do you need In the second coil to get a 6 vac RMS source?

Homework Equations



B_loop=N*mu*I/(2*R)
EMF=d(flux)/dt

The Attempt at a Solution



A) What is the EMF of the base coil?

This should be 0, right? No changing flux is actually going through this coil.

B) what is the EMF of the device coil?

B1 from the outer loop is : N1mu*I/(2*R1), so the RMS EMF through this loop is d/dt(B1*A2)=N1*mu*A2*omega*I_peak/(2*sqrt(2)*R1).

C) how many turns do you need In the second coil to get a 6 vac RMS source?

?

My questions are:

did I do A) right? Is the EMF 0 in the base coil?

And as for part B), the problem states that the resistance of the loop is negligible, and my final answer is in terms of I. Unfortunately the problem gave me the voltage (120V) of the ac power source, so how do I get the current?

And on Part C), I don't see how to factor in the number of coils on the second loop.. did I do part B) correct?

Thanks so much in advance!
 
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  • #2
khfrekek92 said:
A) What is the EMF of the base coil?

This should be 0, right? No changing flux is actually going through this coil.
This is not correct. The base coils is connected to an AC source. There will be an AC current, which will produce the time-varying (AC) magnetic field and induce the EMF in the base coil. Assuming the resistance of the base coil is negligible (perfect inductor), the induced EMF is equal to the source voltage, that is 120 V AC.
khfrekek92 said:
And as for part B), the problem states that the resistance of the loop is negligible, and my final answer is in terms of I. Unfortunately the problem gave me the voltage (120V) of the ac power source, so how do I get the current?
You don't really need the current. but you have to make a second assumption: the field is uniform within the base coil.
In that case, the induced EMF in the base coil is given by: $$ EMF_{BASE} = N_1*A_1* \frac {dB}{dt} $$
I hope I gave you enough hints to answer B and C
Henryk
 
  • #3
Hi HenryK! Thanks for your quick response! So in response to your second hint, I agree that the EMF is proportional to dB/dt. But doesn't dB/dt = d/dt(N1mu*I(t)/(2*R1))? This definitely depends on I, so how do I get a value for this?

Thanks again for your help!
 
  • #4
Hi,

Yes, your formula is correct, but as I said, you don't need to know the value of the current.
I gave you a hint, the EMF induced in the base coil is equal to the applied voltage (true for a perfect inductor) and it is given by
$$ EMF_{BASE} = N_1 * A_1 * \frac{dB}{dt} $$
The EMF of the device coil is equal to
$$ EMF_{DEVICE} = N_2 * A_2* \frac{dB}{dt} $$
Assuming the uniform magnetic field inside, it is the same for both coils. Therefore
$$ \frac {EMF_{BASE}} {N_1 * A_1} = \frac {EMF_{DEVICE}} {N_2 * A_2} $$

It's now easy to get your answers.
 
  • #5
I see exactly what you mean now! I think I understand how it all works now. Thank you so much for your help HenryK, I really appreciate it!
 

Related to Inductive charging: Emf induced in two coil loops

1. What is inductive charging?

Inductive charging is a method of wirelessly transferring energy from one object to another through the use of electromagnetic induction. This technology is commonly used to charge electronic devices without the need for physical contact with a power source.

2. How does inductive charging work?

Inductive charging works by using two coil loops, one in the charging base and one in the device being charged. When an alternating current is passed through the coil in the charging base, it creates a magnetic field. This magnetic field then induces a current in the coil of the device being charged, which can be used to power or charge the device.

3. What are the benefits of inductive charging?

Inductive charging offers several benefits, including convenience, safety, and durability. It eliminates the need for cords and cables, making it easier to charge devices on the go. It also reduces the risk of electric shock since there is no direct contact with an electrical outlet. Additionally, the absence of physical connectors reduces wear and tear on devices, making them more durable.

4. Are there any drawbacks to inductive charging?

One drawback of inductive charging is that it is less efficient than traditional wired charging methods. The energy transfer between the two coil loops can result in some energy loss, leading to longer charging times. Additionally, inductive charging requires specific hardware, so not all devices are compatible.

5. Is inductive charging safe?

Yes, inductive charging is generally considered safe. The magnetic fields used in this technology are low-power, and there is no direct contact with electric outlets or cords, reducing the risk of electric shock. However, it is important to use approved charging bases and devices to ensure safety and avoid any potential hazards.

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