Induced Voltage Equation: Solving for Constant Magnetic Field

In summary, the equation for induced voltage is -dflux/dt= -dB/dt*A or Faraday's law. In this case, the problem involves a circular loop with a radius of 31 cm in a homogeneous magnetic field of 0.3 T being increased at a constant rate by a factor of 2.4 in 13 seconds. The magnitude of the induced emf in the loop during this time can be calculated by finding the change in magnetic field over time, which is (2.4-0.3)/13, and multiplying it by the area of the loop, pi*(.31)^2. The final answer is 0.0167 V. In the second part of the problem, the
  • #1
laxmaster08
19
0
I know the equation for emf: -dflux/dt= -dB/dt*A . In my case everything is constant accept the magnetic field and I am unable to find the equation for that. I know that is what dB is for but that simply does not work in this case.

What is the equation for induced voltage, when everything is constant accept the magnetic field.
 
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  • #2
laxmaster08 said:
What is the equation for induced voltage, when everything is constant accept the magnetic field.
That is the equation (Faraday's law). What is the exact problem?
 
  • #3
Doc Al said:
That is the equation (Faraday's law). What is the exact problem?

A circular loop of radius 31 cm is located in the plane of the paper inside a homogeneous magnetic field of 0.3 T pointing into the paper. It is connected in series with a resistor of 289 Ω. The magnetic field is now increased at a constant rate by a factor of 2.4 in 13 s. Calculate the magnitude of the induced emf in the loop during that time.

I have been using Faraday's. So far I've tried [(2.4-0.3)/13)*pi(.31)^2], [(2.4+0.3)/13)*A], and [(2.4/13)*A]. All in magnitude form.
 
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  • #4
laxmaster08 said:
The magnetic field is now increased at a constant rate by a factor of 2.4 in 13 s.
What's the initial magnetic field before it starts increasing? What's the final magnetic field after 13 seconds? The change in magnetic field during that time?
 
  • #5
Doc Al said:
What's the initial magnetic field before it starts increasing? What's the final magnetic field after 13 seconds? The change in magnetic field during that time?

2.4-0.3=2.1
According to Faraday this divided by the time ,t=13s, all multiplied by the area, A=pi*(.31)^2, should equal the EMF but LON-CAPA does not agree.
Am I missing something? it seems pretty straight forward but it isn't coming out right. btw my answer was 0.0488V
 
  • #6
laxmaster08 said:
2.4-0.3=2.1
According to Faraday this divided by the time ,t=13s, all multiplied by the area, A=pi*(.31)^2, should equal the EMF but LON-CAPA does not agree.
Am I missing something? it seems pretty straight forward but it isn't coming out right. btw my answer was 0.0488V
You are misreading the problem statement. 2.4 is not the final magnetic field, but the factor by which the field is increasing. So once again: What's the final magnetic field after 13 seconds?
 
  • #7
doc al said:
you are misreading the problem statement. 2.4 is not the final magnetic field, but the factor by which the field is increasing. So once again: What's the final magnetic field after 13 seconds?

2.7 ill see if it works
 
  • #8
laxmaster08 said:
2.7 ill see if it works
No. Show how you made that calculation.

FYI: Factor means multiply. If you start out weighing 150 lbs and your weight increases by a factor of 2, what's your final weight?
 
  • #9
Doc Al said:
You are misreading the problem statement. 2.4 is not the final magnetic field, but the factor by which the field is increasing. So once again: What's the final magnetic field after 13 seconds?

Ok that didnt work. So the way its worded it looks like the total time it takes to charge up 2.4 is 13s but I guess it could mean that it charges up 2.4 every second for 13s...Ill try it
 
  • #10
laxmaster08 said:
Ok that didnt work. So the way its worded it looks like the total time it takes to charge up 2.4 is 13s but I guess it could mean that it charges up 2.4 every second for 13s...Ill try it
Nope. Reread my last comment.
 
  • #11
Doc Al said:
Nope. Reread my last comment.

Ok so I am going to multiply my initial 0.3 by a factor of 2.4?
 
  • #12
*over a time period of 13s
 
  • #13
laxmaster08 said:
Ok so I am going to multiply my initial 0.3 by a factor of 2.4?
Yes. At least I hope so!
 
  • #14
nope
 
  • #15
Any ideas? Faraday doesn't say anything about resistance so I'm guessing that pertains to part b of the problem...
 
  • #16
laxmaster08 said:
nope
Nope what?
 
  • #17
Doc Al said:
Nope what?

That doesn't work.
 
  • #18
laxmaster08 said:
That doesn't work.
Show what you did.
 
  • #19
Doc Al said:
Show what you did.

(2.4*0.3)/13)*pi*(.31)^2=0.0167V
 
  • #20
laxmaster08 said:
(2.4*0.3)/13)*pi*(.31)^2=0.0167V
You need the change in magnetic field over time, not just the final field.
 
  • #21
Doc Al said:
You need the change in magnetic field over time, not just the final field.

dB/dt=(2.4-0.3)/(13) ?
 
  • #22
or (2.4*0.3)-(0.3))/13
 
  • #23
Success! That problem had really sneaky wording.
 
  • #24
laxmaster08 said:
Success! That problem had really sneaky wording.
Finally! :cool:
 
  • #25
Now the second part looks much trickier. It looks like I will have to use right hand rule...
"Calculate the average induced voltage when the magnetic field is constant at 0.72 T while the loop is pulled horizontally out of the magnetic field region in 4.1 s"
 
  • #26
Haha yah that took quite a while. If your out ill understand I can probably figure this one out...probably.
 
  • #27
What does it mean by pulled out of the magnetic field? Does that mean a force due to current in the loop is pushing it?
 
  • #28
Will this use Faraday's?
 
  • #29
Nvm that was cake! thanks man peace out
 

1. What is the induced voltage equation?

The induced voltage equation is a mathematical expression that relates the change in magnetic flux through a conductor to the induced electromotive force (EMF) or voltage. It is represented as E = -N(dΦ/dt), where E is the induced voltage, N is the number of turns in the conductor, and dΦ/dt is the rate of change of magnetic flux.

2. How is the induced voltage equation used to solve for a constant magnetic field?

The induced voltage equation can be rearranged to solve for a constant magnetic field by dividing both sides by -N and integrating with respect to time. This results in the equation Φ = -N∫E dt, where Φ is the magnetic flux through the conductor. By knowing the value of the induced voltage and the number of turns in the conductor, the constant magnetic field can be calculated.

3. What is the significance of the negative sign in the induced voltage equation?

The negative sign in the induced voltage equation represents the direction of the induced EMF or voltage. It follows Lenz's law, which states that the direction of the induced current is always such as to oppose the change in magnetic flux that produced it. This means that if the magnetic flux is increasing, the induced voltage will be in the opposite direction to try to decrease the change in flux.

4. How can the induced voltage equation be applied in real-world situations?

The induced voltage equation has many practical applications, such as in generators and transformers. In generators, the rotation of a coil in a magnetic field results in a changing magnetic flux and induces a voltage, which can then be used to produce electricity. In transformers, the changing magnetic field from an alternating current induces a voltage in a nearby coil, allowing for the transfer of electrical energy between circuits.

5. What are the limitations of the induced voltage equation?

The induced voltage equation assumes ideal conditions, such as a uniform magnetic field and a perfect conductor. In real-world situations, these conditions may not be met, leading to errors in the calculated induced voltage. Additionally, the equation does not account for factors such as resistance, which can affect the induced voltage and must be considered in practical applications.

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