TA: Calculating Induced EMF in a Square Loop with a Uniform Magnetic Field

PS LAW:The magnetic field is created by a current. So if a current is changing in a wire, it will create a changing magnetic field. This changing magnetic field will induce an emf in a nearby loop of wire. In summary, the conversation discusses a problem concerning induced emf in a high school AP class. They mention a loop of wire with a magnetic field directed into the page and the back of the book providing the answer. They also mention important concepts such as Faraday's law, Lenz's law, and Amps law in relation to finding the induced emf.
  • #1
Giuseppe
42
0
Hey, I'm in a high school AP class and am stuck! Can anyone help me with this problem concerning induced emf? I would surely appreciate it.

There is a loop of wire, shaped like a square. Each side is 20 cm long.
There is a magnetic field directed into the page.

What would be the way of finding out what the induced emf in the loop. The back of the book says that the answer is 1.40 x 10^-4 Volts.
 
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  • #2
Well, how is an induced current 'created'. I mean, what will you need to do, so that a current is generated in the loop ? What will have to change ?

regards
marlon

ps : LENZ'S LAW (or more generally, the Faraday induction law)is the direction you are looking for.
 
  • #3
Giuseppe said:
Hey, I'm in a high school AP class and am stuck! Can anyone help me with this problem concerning induced emf? I would surely appreciate it.

There is a loop of wire, shaped like a square. Each side is 20 cm long.
There is a magnetic field directed into the page.

What would be the way of finding out what the induced emf in the loop. The back of the book says that the answer is 1.40 x 10^-4 Volts.
You are missing some important information such as the magnitude of the field and either its rate of change or the motion of the loop.

The induced emf is given by Faraday's law:

[tex]V_{induced} = \frac{d\phi}{dt}[/tex]

In this case, the flux is BA where A is the area of the square loop. How does this change with time?

AM
 

1. What is induced emf in a loop?

Induced emf in a loop, also known as induced electromotive force, is the voltage created in a conducting loop when the magnetic flux through the loop changes. This change in flux can be caused by a changing magnetic field or by the motion of the loop in a stationary magnetic field.

2. How is induced emf calculated?

The induced emf in a loop can be calculated using Faraday's Law of Induction, which states that the magnitude of induced emf is equal to the rate of change of magnetic flux through the loop. It can be represented by the equation E = -N(dΦ/dt), where E is the induced emf, N is the number of turns in the loop, and dΦ/dt is the change in magnetic flux over time.

3. What factors affect the magnitude of induced emf?

The magnitude of induced emf in a loop is influenced by several factors, including the strength of the magnetic field, the rate of change of the magnetic field, the number of turns in the loop, and the area of the loop. Additionally, the orientation of the loop with respect to the magnetic field can also affect the induced emf.

4. How is induced emf related to Lenz's Law?

Lenz's Law is a basic law of electromagnetism that states that the direction of induced emf is such that it opposes the change in magnetic flux that caused it. This law is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only converted from one form to another. Therefore, induced emf acts to resist changes in magnetic flux, leading to the concept of self-inductance in circuits.

5. What are some real-world applications of induced emf in a loop?

Induced emf in a loop has many practical applications, including in electric generators, transformers, and induction cooktops. It is also the basis for many technologies, such as wireless charging and electromagnetic levitation. Additionally, the concept of induced emf is used in a variety of scientific and engineering fields, including power systems, motors, and magnetic sensors.

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