What Is the Induced EMF in the Coil?

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Homework Help Overview

The discussion revolves around calculating the induced electromotive force (EMF) in a coil placed within a solenoid, with specific parameters regarding the solenoid's dimensions and the current variation over time.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula for the magnetic field in the solenoid and its application to find the induced EMF. There are questions about the correctness of the magnetic field calculation and the method for determining the rate of change of the magnetic field.

Discussion Status

Some participants have provided formulas and attempted to clarify the magnetic field's calculation, while others express uncertainty about their results and seek further assistance. There is an ongoing exploration of the assumptions made in the calculations.

Contextual Notes

Participants are working under the constraints of the problem's parameters and the specific formulas related to solenoids and induced EMF. There is a noted confusion regarding the application of these formulas and the assumptions about the solenoid's length.

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A solenoid of length 45 cm has 340 turns of radius 2.2 cm. A tightly wound coil with 16 turns of radius 4.4 cm is at the center of the solenoid. The axes of the coil and solenoid coincide. Find the emf induced in the coil if the current in the solenoid varies according to I=4.6sin(50∏t)A.

Answer: __________cos(50∏t) mV

Comments:
I can't seem to find the correct answer for the magnetic field of the solenoid.
The formula I use is:
B=0.5μ0nI(sinθ2-sinθ1)
The area to use for all equations is the area of the solenoid since it is the area of magnetic field lines felt by the coil.
The flux, denoted ∅ is: ∅=BAcosσ and σ=0o, therefore ∅=BA
and the EMF=-N(d∅/dt)=-NA(dB/dt)

I really appreciate any help, thank you!
 
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B on the axis and at the centre of a 'long' solenoid is given by B = \mu_{o}nI where n = number of turns/length of solenoid.
 
Last edited:
Assuming the solenoid is long an using that formula, my answer is wrong. Is there anything missing to the comments I added for solving this problem?
 
Can you show the working for dB/dt?
 

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