A 59.0 -turn, 4.10-cm-diameter coil with R = 0.530 {\Omega} surrounds a 1.70-cm-diameter solenoid. The solenoid is 21.0 cm long and has 170 turns. The 60 Hz current through the solenoid is I_sol = (.470A)*sin(2*pi*f*t). I guess f is the frequency.
Find the value of I_coil, the induced current in the coil at time t= 1.85 seconds?
I tried plugging into solenoid equation getting field then using that field to find induced current but am not getting it.
what did you plug into the solenoid equation? What did you take as dB/dt?
Let me see you work, I suspect the error is in the detail.
ok for dB/Dt I get .18025cos(2pift). for induced emf its Area*dB/dt*N(turns). ive tried it with a problem I know and it works fine. at the end do i just plug in the given t into the equation. Please could you work it out i think its calculation but i cant find it. I use B=(u*N*Isol)/L this gives magnetic field for solenoid. B= (4pie-7*170*.470*sin(2pift)/.21
this gives 4.781e-4*sin(2pift)
dB/dT is .18025 cos(2pift).
the area in the calculation is the area between the solenoid and coil. so its pi*((.041/20)^2-(.017/2)^2)=area. so this area times the dB/dT times number of turns 59 should equal induced emf . then that divided by resistance should be it. could you work it out and tell me what you get. I keep getting 20.3 mA
please help by 9am.
nvm found it elsewhere. turns out i had my calc in degrees instead of radians. don't you just hate when that happens.
To find the value of the induced current in the coil at time t = 1.85 seconds, you need to use Faraday's law of electromagnetic induction. This law states that the induced electromotive force (emf) in a closed loop is equal to the negative rate of change of magnetic flux through the loop.
1. Calculate the magnetic flux change through the coil:
The magnetic flux through a coil is given by the product of the magnetic field (B) and the area (A) the coil encloses. In this case, the coil surrounds the solenoid, so the magnetic flux through the coil is due to the changing magnetic field produced by the solenoid.
The magnetic field produced by the solenoid at the location of the coil can be calculated using the formula:
B = μ₀ * N * I_sol / L,
where μ₀ is the permeability of free space (μ₀ = 4π × 10^-7 T·m/A), N is the number of turns in the solenoid (N = 170), I_sol is the current through the solenoid, and L is the length of the solenoid.
In this case, the current through the solenoid is given by:
I_sol = (0.470A) * sin(2πf * t).
The length of the solenoid is 21.0 cm = 0.21 m.
2. Determine the change in magnetic flux:
The change in magnetic flux through the coil can be calculated by subtracting the initial flux from the final flux. At time t = 0 seconds, the induced current in the coil is zero, so there is no initial magnetic flux. At t = 1.85 seconds, we need to find the final magnetic flux.
3. Calculate the final magnetic flux:
The final magnetic flux through the coil is given by:
Φ_final = B * A_coil,
where A_coil is the area of the coil.
The area of the coil can be calculated using the formula:
A_coil = (π/4) * [(d_outer^2) - (d_inner^2)],
where d_outer is the outer diameter of the coil and d_inner is the inner diameter of the coil.
In this case, d_outer = 4.10 cm = 0.041 m, and d_inner = 1.70 cm = 0.017 m.
4. Calculate the induced current:
The induced electromotive force (emf) in the coil is given by Faraday's law, which can be written as:
emf = -N * (dΦ/dt),
where N is the number of turns in the coil and dΦ/dt is the change in magnetic flux with respect to time.
We want to find the induced current (I_coil), which can be calculated using Ohm's law:
I_coil = emf / R,
where R is the resistance of the coil.
In this case, R = 0.530 Ω.
Now, you can plug in the values and calculate the induced current in the coil at t = 1.85 seconds using the steps outlined above.