Magnitude of changing magnetic field

In summary, the problem involves a square loop with a resistance of 4.00 Ω and an area of 600 cm^2. It is placed in a uniform magnetic field directed out of the page and contains a 12-volt battery. At the instant shown, there is no net current in the loop. The question asks for the rate of change of the magnitude of the magnetic field, which can be found using the equation ΔB/Δt = ε/NA, where ε is the emf and N is the number of turns in the loop. After correcting for the direction of the induced current, the answer is -200 T/s.
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Homework Statement


A square loop consists of a single turn with a resistance of 4.00 Ω. The loop has an area of 600 cm^2, 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 below.
C:\Users\Michael\Pictures\20-p-044.gif
At the instant shown in the figure, there is no net current in the loop. At what rate is the magnitude of the magnetic field changing?

Homework Equations


Φ=BAcosθ
ε=-NΔΦ/Δt


The Attempt at a Solution


ε=-NΔΦ/Δt
ε=-NΔBAcosθ/Δt, A is constant so
ε=-NAΔB/Δt
ΔB/Δt=ε/NA, negative sign is removed because only magnitude is asked for.
ΔB/Δt=12V/(1)(0.06m^2)=200T/s

I worked this out and it turned out to be wrong. I put in 12V as the emf as I thought that the total voltage should be the same as there is no net current in the loop, however that is the only part of the problem that I am uncertain about. The answer must be in T/s.
Thank you in advance for the help.
 
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Never mind, I got it. It wasn't asking for what was the magnitude of the change in magnetic field but the rate of change. Since the induced current from the field will be opposite to the that of that in the loop, the answer should be negative. So I did it correctly, just misread what the problem was asking for.

Thank you!
 

FAQ: Magnitude of changing magnetic field

1. What is the magnitude of a changing magnetic field?

The magnitude of a changing magnetic field refers to the strength or intensity of the field as it changes over time. It is measured in units of tesla (T) or gauss (G).

2. How is the magnitude of a changing magnetic field determined?

The magnitude of a changing magnetic field can be determined using a device called a magnetometer, which measures the strength of the magnetic field at a specific location. It can also be calculated using mathematical equations based on the distance from the source of the field and the rate of change over time.

3. Why is the magnitude of a changing magnetic field important?

The magnitude of a changing magnetic field is important because it affects the behavior of charged particles and can have significant impacts on the environment and technology. It is also a key factor in understanding and predicting phenomena such as geomagnetic storms and auroras.

4. How does the magnitude of a changing magnetic field impact living organisms?

The magnitude of a changing magnetic field can potentially impact living organisms, as some species have been found to use Earth's magnetic field for navigation and orientation. In addition, changes in the magnetic field can affect the Earth's ionosphere, which can disrupt communication and navigation systems used by humans and animals.

5. Can the magnitude of a changing magnetic field be controlled?

In some cases, the magnitude of a changing magnetic field can be controlled using devices such as electromagnets. However, the Earth's magnetic field is constantly changing and its magnitude cannot be controlled by humans. Scientists are still researching ways to better understand and predict changes in the Earth's magnetic field.

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