What Is the Rate of Change of the Magnetic Field in This Circuit?

In summary, when the polarity of the battery is reversed, the magnetic field through the loop is still changing at the rate you calculated, but the battery now contributes its 12v so that the two voltages add.
  • #1
aokidopi
29
0
1. http://www.webassign.net/userimages/ch20_prob20_40.jpg?db=v4net&id=110544

A square loop consists of a single turn with a resistance of 5.00 ohms. The loop has an area of 500 cm2, and has a uniform magnetic field passing through it that is directed out of the page. The loop contains a 12-volt battery, connected as shown in the figure above.
(a) At the instant shown in the figure, there is no net current in the loop. At what rate is the magnetic field changing? Use a positive sign if the field is increasing and magnitude, and a negative sign if the field is decreasing in magnitude.

T/s

(b) If the polarity of the battery was reversed, and the magnetic field was still changing at the rate you calculated above, what would the magnitude of the net current through the loop be?

A



2. Faraday's Law and Magnetic Flux
Flux=ABcos(theta)
emf=N*change in flux/change in time
V=IR




3. I was able to solve for part A using a combination of the first two equations to solve for Magnetic field/ time.

However, I am having trouble understanding the second part. If the rate of change in magnetic field is same, isn't emf still 12V and the resistance 5 ohms? I know that 12/5 for the ohm's law does not result in the correct solution.


Thanks for your help.
 
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  • #4
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  • #5
Voltages in series add or subtract. The loop generates the same emf as before, but now the battery contributes its 12v so that the two voltages add.

What is the correct answer?
 
  • #6
How do you solve for a?

I did the following:

induced emf e = - N dφ/dt

flux φ = B * A ( A is the area of loop)

e = - 1 * d( B * 0.5m^2 ) /dt

-12 = - 0.05 * dB/dt

dB/dt = 12/.05 = 240 T/s

Why is this incorrect? It asks for magnitude so sign shouldn't matter anyways.
 
  • #7
ment2byours said:
How do you solve for a?

I did the following:

induced emf e = - N dφ/dt

flux φ = B * A ( A is the area of loop)

e = - 1 * d( B * 0.5m^2 ) /dt

-12 = - 0.05 * dB/dt

dB/dt = 12/.05 = 240 T/s

Why is this incorrect? It asks for magnitude so sign shouldn't matter anyways.

Hi ment2byours, are you in the same class as aokidopi? How do you know what the correct answer is?

Using this relation,
induced emf e = - N dφ/dt
you can find dφ/dt. Beyond that, I don't think there is much you can say. Though you can definitely determine the instantaneous current.
 
  • #8
aokidopi said:
However, I am having trouble understanding the second part. If the rate of change in magnetic field is same, isn't emf still 12V and the resistance 5 ohms? I know that 12/5 for the ohm's law does not result in the correct solution.
There are two voltage sources present. The coil is generating a voltage, and the battery is also contributing a voltage. These can either add, or subtract.
 
  • #9
Oh, I am not sure if I'm in the same class or not and my problem is that I DON'T know what the correct answer is BUT I do know mines is the wrong one.

Thanks for the help let me think/try it now.
 
  • #10
I still don't get it. Is my math wrong?
 
  • #11
240 T/s looks right.
 
  • #12
ment2byours said:
I still don't get it. Is my math wrong?

you put down 0.5m^2 for the area when it should be 5m^2 since you are converting from cm to m
 
  • #13
oh yeah i was given 500cm^2 but that still converts to 0.05m^2 so it was just a slip of the hand, I still don't see what else is wrong.
 
  • #14
you need to include the minus sign!
 
  • #15
my problem asks for magnitude.
 

Related to What Is the Rate of Change of the Magnetic Field in This Circuit?

1. What is a magnetic field circuit problem?

A magnetic field circuit problem refers to a situation where there is a disruption or malfunction in the flow of magnetic fields in a closed loop or circuit. This can lead to issues such as loss of power or interference in electronic devices.

2. What are the main causes of magnetic field circuit problems?

The main causes of magnetic field circuit problems can include faulty wiring, damaged components, or external factors such as nearby power lines or strong magnetic fields.

3. How can magnetic field circuit problems be diagnosed?

Magnetic field circuit problems can be diagnosed by using specialized equipment such as multimeters or gaussmeters to measure the strength and direction of magnetic fields. Visual inspections and testing of individual components can also help identify the issue.

4. What are some solutions for fixing magnetic field circuit problems?

The solution for fixing a magnetic field circuit problem will depend on the specific cause identified. It may involve replacing damaged components, re-routing wiring to avoid interference, or installing shielding materials to block external magnetic fields.

5. How can magnetic field circuit problems be prevented?

To prevent magnetic field circuit problems, it is important to carefully plan and design the circuit to minimize the risk of interference. Regular maintenance and inspections can also help identify and address any potential issues before they become major problems.

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