Magnetic Field with Time Dependence

In summary, the induced EMF in the coil at t=7.5ms in mV is 1637.07 mV. This was calculated using the formula |EMF|= N*|change in magnetic flux/change in time|. First, the area of the coil was found to be 0.001385m^2. Then, the slope of the magnetic field between 5 and 10 ms was determined to be -0.006 T/ms. Using this slope, the rate of change of the flux was found to be -0.00831 T/s. Finally, this rate of change was multiplied by the number of turns (197) to get the induced EMF in volts, which was then converted to
  • #1
deenuh20
50
0

Homework Statement



A magnetic field with the time dependence shown in the figure below is at right angles to a N=197 turn circular coil with a diameter of d=4.2 cm.


What is the induced EMF in the coil at t=7.5ms in mV?

See attached graph


Homework Equations



|EMF|= N*|change in magnetic flux/change in time|



The Attempt at a Solution



First Attempt:
I first found Area by pi*(.042m/2)^2 and got 0.001385m^2. Then, I found the slope of the line between 5 and 10 ms, which was -0.006 T/ms. Then, I multiplied this slope by 7.5ms to see what the magnetic field at 7.5ms was, and I got -0.45T. Then, I used this value to find the magnetic flux which was (0.001385m^2)(-0.045T) and got -6.235*10^-5. Then, I took this value, divided by 7.5ms, and got -0.00831. Then, I multiplied this by 197 and got -1.63707 V. I divided this by 1000 and got -0.001637mV, but this answer is not being accepted.
 

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  • #2
deenuh20 said:
First Attempt:
I first found Area by pi*(.042m/2)^2 and got 0.001385m^2.
Good.
Then, I found the slope of the line between 5 and 10 ms, which was -0.006 T/ms.
All good, so far. And this is almost all you need.

Hint: You've already calculated the rate of change of the field, so what's the rate of change of the flux?

(The flux doesn't matter--only the rate of change of the flux.)
 
  • #3
To find the rate of change of the flux, I did:

(B @ 10ms * Area) - (B @ 5ms * Area) all divided by (10ms-5ms)
(-0.01T*0.001385)-(0.02T*0.001385)/(5ms) and got 4.155*10^-5 as the rate of change of the flux

I then multiplied 4.155*10^-5 by 197, and got 0.008185, which I then divided by 1000, and got 8.18535mV, however, this is still not the right answer.

Is my reasoning flawed or am I missing an essential step?
 
  • #4
deenuh20 said:
To find the rate of change of the flux, I did:

(B @ 10ms * Area) - (B @ 5ms * Area) all divided by (10ms-5ms)
(-0.01T*0.001385)-(0.02T*0.001385)/(5ms) and got 4.155*10^-5 as the rate of change of the flux
Your reasoning is fine; check your arithmetic.
 
  • #5
Ok, let's try this step by step:

deenuh20 said:
To find the rate of change of the flux, I did:

(B @ 10ms * Area) - (B @ 5ms * Area) all divided by (10ms-5ms)
(-0.01T*0.001385)-(0.02T*0.001385)/(5ms) and got 4.155*10^-5 as the rate of change of the flux

I redid my arithmetic here, and as the rate of change of flux, I now got -0.00831

Is this correct?

Also, Thank you very much for your help!:smile:
 
  • #6
Looks good to me. (Units: T/s)
 
  • #7
deenuh20 said:
I redid my arithmetic here, and as the rate of change of flux, I now got -0.00831

Ok, now that I have the rate of change of flux, in order to find the induced EMF, in mV:

I multiplied the rate of change of flux by the number of turns (197)

(-0.00831 T/s)(197)= -1.63707 V

then to get mV: -1.63707 V/1000 = -0.001637 mV

Correct?


If this is the correct way to do it, it is still the wrong answer when I enter it in my homework online :confused:
 
  • #8
deenuh20 said:
I multiplied the rate of change of flux by the number of turns (197)

(-0.00831 T/s)(197)= -1.63707 V

then to get mV: -1.63707 V/1000 = -0.001637 mV


I got it! I figured out what I was doing wrong. I had to divide by 10^-3, not 1000, and got 1637.07 mV, which was the right answer. Thanks for all your help!
 
  • #9
deenuh20 said:
then to get mV: -1.63707 V/1000 = -0.001637 mV
Check this step. (How many mV in a Volt? :wink: )

(edit: Looks like you figured that out on your own!)
 
Last edited:

1. What is a magnetic field with time dependence?

A magnetic field with time dependence is a type of magnetic field that changes over time. This can be due to a variety of factors, such as the movement of charged particles or the presence of a changing electric field. In this type of field, the strength and direction of the magnetic field vary as time passes.

2. How is a magnetic field with time dependence created?

A magnetic field with time dependence can be created in several ways. One common method is by passing an electric current through a wire, which creates a magnetic field around the wire. This field can then change over time as the current or the wire's position is altered. Another way is through electromagnetic induction, where a changing magnetic field can induce a magnetic field in a nearby conductor.

3. What are some real-world examples of magnetic fields with time dependence?

Magnetic fields with time dependence are present in many natural and man-made systems. Some examples include the Earth's magnetic field, which is constantly changing due to the movement of molten iron in the planet's core, and the magnetic field generated by power lines, which can vary with the amount of current flowing through them. Other examples include magnetic fields produced by motors, generators, and MRI machines.

4. How is a magnetic field with time dependence measured?

A magnetic field with time dependence can be measured using a device called a magnetometer. This instrument can detect changes in the strength and direction of a magnetic field and display it on a digital readout. Some magnetometers also have the ability to record and graph the changes over time, providing a visual representation of the field's time dependence.

5. What are the applications of magnetic fields with time dependence?

Magnetic fields with time dependence have many practical applications in various fields, including physics, engineering, and medicine. They are used in generators to produce electricity, in motors to convert electricity into motion, and in MRI machines to create detailed images of the body's internal structures. They are also essential for technologies such as compasses, which use the Earth's magnetic field to determine direction, and magnetic levitation trains, which use time-varying magnetic fields to create lift and propulsion.

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