Faraday's Law (Flux on one coil due to current through another Coil)

In summary, this conversation discusses the calculation of magnetic flux and electric fields in a system with two aligned coils of wire. The direction of the electric field and magnetic flux is determined at a specific time interval, and equations are provided for calculating the emf and non-Coulomb electric field. The conversation also mentions the use of symbolic calculations and the importance of considering all turns of the coils in the calculations.
  • #1
iDFLO
2
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Homework Statement


23-076-two_coils_in_line_noI_sym.jpg


There are a lot of numbers in this problem. Just about the only way to get it right is to work out each step symbolically first,and then plug numbers into the final symbolic result.

Two coils of wire are aligned with their axes along the z-axis,as shown in the diagram. Coil 1 is connected to a power supply and conventional current flows counter-clockwise through coil 1, as seen from the location of coil 2. Coil 2 is connected to a voltmeter. The distance between the centers of the coils is 0.14 m.
Coil 1 has N_1 = 565 turns of wire, and its radius is R_1 =0.07 m. The current through coil 1 is changing with time. At t=0 s, the current through coil 1 is I_0 = 15 A. At t=0.4 s,the current through coil 1 is I_0.4 =6 A.
Coil 2 has N_2 = 280 turns of wire, and its radius is R2 = 0.03 m.


Inside coil 2, what is the direction of – d/dt during this interval?
+Z (correct)
What is the direction of the electric field inside the wire of coil 2, at a location on the top of coil 2?
-X(correct)
At time t=0, what is the magnetic flux through one turn of coil 2? Remember that all turns of coil 1 contribute to the magnetic field. Note also that the coils are not very far apart(compared to their radii), so you can't use an approximate formula here.
At t=0 Phi_1 turn = ? T m2

***THIS IS WHERE I'M STUCK*** :confused:

At t=0.4 s, what is the magnetic flux through one turn ofcoil 2?
At t=0.4 s Phi_1 turn = ? T m2


What is the emf in one turn of coil 2 during this timeinterval?
|emf1 turn| = ? V

The voltmeter is connected across all turns of coil 2. What is thereading on the voltmeter during this time interval?
voltmeter reading is ? V

During this interval, what is the magnitude of the non-Coulombelectric field inside the wire of coil 2? Remember that the emfmeasured by the voltmeter involves the entire length of the wiremaking up coil 2.
ENC = ? V/m

At t=0.5 seconds, the current in coil 1 becomes constant, at 5 A. Which of the following statements are true?
1. The electric field inside the wire of coil 2 now points in the opposite direction.
2. The voltmeter now reads 0 V.
3. The voltmeter reading is about the same as it was at t=0.4 seconds.
4. The electric field inside the wire of coil 2 is now 0 V/m.

Homework Equations


I = dV/R
dV= Emf
Emf= -N*dPhi_mag/dt = -N*(d/dt)(B*n*dA)
Phi = B*n*dA

N=number of turns, n = nhat normal unit vector to area.
R = resistance

The Attempt at a Solution



If I had a resistance I know I could find emf and from there find the flux phi, but without it I'm stuck and don't know what to do.
 
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  • #2
iDFLO said:
At time t=0, what is the magnetic flux through one turn of coil 2? Remember that all turns of coil 1 contribute to the magnetic field. Note also that the coils are not very far apart(compared to their radii), so you can't use an approximate formula here.
At t=0 Phi_1 turn = ? T m2

***THIS IS WHERE I'M STUCK*** :confused:

No dimensions are given on the coils so I suppose you will assume that the coils have no width in the z direction.

It looks like you are going to have to calculate the B field due to coil 1 and integrate that at coil 2 to find the flux at coil 2. Do you remember what sort of field a current in a loop generates?
 
  • #3
After pondering about this question for the better part of half an hour, while watching SC2 :), I was able to figure it all out! :D

for the first two parts where it asks for the flux, phi.
I used the equation Phi = B*n.hat*dA
where B_loop = N * (μ_0/4*pi) * (2*pi*r^2*I) / (z^2+r^2)^(3/2)
where N, I, and r belong to the current carrying wire. and z is the distance between the center of both coils.
Then Phi = B * dA
where dA is the cross sectional area of coil 2.

Emf for a single loop was then found using Emf = -dPhi/dt
dPhi would be Phi(0.4) - Phi(0) and dt is 0.4 - 0

Emf for the whole loop was found by multiplying the previous answer times the number of loops in coil 2. Emf(tot) = Emf(single loop) * N

E_nc was found by using E_nc = Emf / (2*pi*r*N)
where E_nc is the non-column electric field. r is the radius of coil 2, and N is the number of turns in coil 2. 2*pi*r*N = the total length of the coil

Hope this helps other people! :D
 

FAQ: Faraday's Law (Flux on one coil due to current through another Coil)

How does Faraday's Law work?

Faraday's Law states that when there is a change in magnetic flux through a closed loop, an electromotive force (EMF) is induced in that loop. This can be achieved by either changing the magnetic field strength or by moving the loop in the magnetic field.

What is flux?

Flux is a measure of the strength of a magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of webers (Wb).

How does current in one coil affect the flux in another coil?

When a current flows through one coil, it generates a magnetic field around it. This magnetic field then passes through the other coil, causing a change in magnetic flux. This change in flux induces an EMF in the second coil, according to Faraday's Law.

What factors affect the magnitude of the induced EMF?

The magnitude of the induced EMF depends on the rate of change of magnetic flux, the number of turns in the coil, and the strength of the magnetic field. Additionally, the orientation of the coils relative to each other also plays a role in the induced EMF.

What are some real-world applications of Faraday's Law?

Faraday's Law has many practical applications, including power generation through electromagnetic induction, electric motors and generators, transformers, and induction cooktops. It also plays a crucial role in technologies such as wireless charging, electromagnetic brakes, and magnetic levitation trains.

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