Calculating Magnetic Fields and Induced EMFs: Help Needed!

In summary, the conversation is about measuring the magnetic fields produced by power lines carrying 50Hz alternating current. A coil with 1500 turns and an area of 5cm^2 is constructed for this purpose. The magnitude of the magnetic field at the coil is found using the equation B = [N(mu_0)I]/2R. The question also asks for the magnitude of the induced emf in the coil, which can be found using the change in flux over time. The current equation as a function of time is necessary for this calculation. The conversation also clarifies that the magnetic field is not constant.
  • #1
WY
28
0
Hey
I'm wondering if someone can help me out with this question.

Q: In order to measure the magnetic fields produced by the power lines carrying 50Hz alternating current, a coil consisting of 1500 turns of area 5cm^2 as constructed. Suppose that there is a single power line carrying a current which has an amplitude of 800A and that the coil is 10m from the wire.
a) What is the magnitude of the magnetic field at the coil
I found this using B =[N(mu_0)I]/2R
b) What is the magnitude of the induced emf in the coil?

I'm stumped on B :confused: could anyone point me in the right direction? I was using the idea that change in flux over time can be used to find induced emf and that in an alternating curret dI/dt=2*pi*f*I - but the problem is that i don't know where to go from there.

Thanks in advance!
 
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  • #2
The magnetic field is not constant.
Write the equation for the current as a function of time.
 
  • #3
thanks for the quick reply - but i don't quite understand how this ties in with finding the emf using the change in flux over the change in time.
 
  • #4
oh i see now! sorry - I wasn't thinking properly! Thanks again :)
 

1. How do I calculate the magnetic field strength at a given point?

To calculate the magnetic field strength at a given point, you will need to know the current flowing through a wire or coil, the distance from the wire or coil to the point, and the permeability of the surrounding material. You can then use the formula B = (μ0 * I) / (2π * r), where B is the magnetic field strength, μ0 is the permeability of free space, I is the current, and r is the distance from the wire or coil to the point.

2. What is the difference between magnetic field strength and magnetic flux density?

Magnetic field strength and magnetic flux density are related but not the same. Magnetic field strength refers to the amount of force exerted on a unit charge moving through a magnetic field, while magnetic flux density refers to the amount of magnetic flux passing through a unit area. In simpler terms, magnetic field strength measures the intensity of the magnetic field, while magnetic flux density measures the density of the field lines.

3. How do I calculate the induced EMF in a coil?

You can calculate the induced EMF in a coil by using Faraday's law of induction, which states that the induced EMF is equal to the negative rate of change of magnetic flux through the coil. This can be expressed as E = -dΦ/dt, where E is the induced EMF, Φ is the magnetic flux, and t is time. This formula can also be written as E = -N * dΦ/dt, where N is the number of turns in the coil.

4. What is Lenz's law?

Lenz's law is a fundamental law of physics that states that the direction of an induced current in a conductor will always be such that it opposes the change that caused it. In simpler terms, an induced current will always flow in a direction that creates a magnetic field that opposes the change in the magnetic field that induced it. This law is important in understanding and predicting the behavior of electromagnetic induction.

5. Can you provide an example of calculating magnetic fields and induced EMFs?

One example of calculating magnetic fields and induced EMFs is when a wire carrying a current of 2 amps is placed near a loop of wire with 100 turns and a radius of 0.5 meters. The distance between the wires is 0.1 meters. Using the formula B = (μ0 * I) / (2π * r), we can calculate the magnetic field strength at the center of the loop to be B = (4π * 10^-7 * 2) / (2π * 0.1) = 4π * 10^-6 Tesla. To calculate the induced EMF in the loop, we can use the formula E = -N * dΦ/dt, where N is 100 and dΦ/dt is the change in magnetic flux. If the current in the wire is suddenly increased to 4 amps, the magnetic flux through the loop will also double, resulting in an induced EMF of E = -100 * (2 * Φ - Φ) / t = -100 * Φ / t. The negative sign indicates that the induced current will flow in a direction that opposes the change in magnetic flux.

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