Magnetic flux / induced emf problem

In summary: You're a life savor!In summary, the small coil has a field of .0113T which creates a flux of 1.42E-5 amps through it.
  • #1
tombroz
5
0

Homework Statement


A single coil with a radius of .02m is placed inside a 3m long solenoid that has 600 turns. The radius of the solenoid is 0.15m. The plane of the coil is perpendicular to the axis of the solenoid. The solenoid is connected to a battery, an ammeter and a switch. The ammeter reachs 5A in 0.2 seconds and remains constant.

a) What is the change in the magnetic flux across the small loop?
b) What is the average induced emf in the small loop?
c) Another solenoid has an inductance of 8.0 henries and a resistance of 2.772 Ohms. It is connected to a battery and a switch. How long does it take for the current to reach half of its maximum value after the switch is closed?

Ahhh... crap. This problem is hard for me.

Homework Equations



I know the equation for magnetic flux is:
Phi = (B*A*cosPhi)
B is the magnetic field, A is area.

The Attempt at a Solution


I don't know how the coil relates with the solenoid. Should I first figure out what is going on inside the solenoid? Then from there I could figure out the emf of the single coil? I'm lost. I'm having trouble conceptualizing this problem. Any help is greatly appreciated. Thanks!
 
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  • #2
tombroz said:
I don't know how the coil relates with the solenoid. Should I first figure out what is going on inside the solenoid?
Absolutely! What's the field inside the solenoid? That's the field that is creating the flux through the coil.
 
  • #3
Great.

The formula to find the field inside of a solenoid is B = Mu*Number of turns*Length of solenoid*I. Using this, I found the field to be 0.0113T.
Magnetic flux = BAcosPhi
When plugging in my B value from the field inside the solenoid and the area (Pi*r^2) of the coil and cos 0, my value is off. I get 1.42E-5. What I'm looking for is 1.58E-6.

Can you help me? Where did I go wrong?
 
  • #4
tombroz said:
The formula to find the field inside of a solenoid is B = Mu*Number of turns*Length of solenoid*I.
The correct formula is μ*(N/L)*I.
 
  • #5
Ahh yes...

using Mu*(N/L)*I, I returned a value of .0013 which fit nicely into my change in magnetic flux equation to give me the correct answer.

Thanks a lot!
 

1. What is magnetic flux?

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

2. How is magnetic flux related to induced emf?

Induced emf (electromotive force) occurs when there is a change in magnetic flux over time. This change in flux creates an electric field, which generates a voltage and thus an emf. The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux.

3. What factors affect the magnitude of induced emf?

The magnitude of induced emf is affected by the strength of the magnetic field, the area through which the field passes, the angle between the magnetic field and the area, and the rate of change of the magnetic field.

4. How is the direction of induced emf determined?

The direction of induced emf is determined by Lenz's Law, which states that the direction of induced current or emf is always such that it opposes the change that caused it. This means that the direction of the induced emf is always opposite to the direction of the change in magnetic flux.

5. What are some real-life applications of magnetic flux and induced emf?

Magnetic flux and induced emf are used in a variety of devices, such as generators, transformers, and electric motors. They are also used in technologies like magnetic levitation trains and magnetic resonance imaging (MRI) machines. Additionally, they play a crucial role in the Earth's magnetic field and its protection from harmful solar radiation.

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