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In summary, the problem involves a solenoid with 10 turns/cm and a circular loop with 5 turns and an area of i cm^2. The loop is positioned at a 37 degree angle to the solenoid's axis. The goal is to find the magnitude of the average induced emf when the current in the solenoid increases by 25% in 0.1 seconds. There is some confusion about the relevance of the solenoid's area, as the magnetic field inside the solenoid is radially uniform.
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## Homework Statement

A solenoid has 10 turns/cm and carries a 4-A current. A circular loop with 5 turns of area i cm^2 lies within the solenoid with its axis at 37 degrees to the axis of the solenoid. Find the magnitude of the average induced emf if the current increases by 25% in .1 seconds.

I got the right answer, but something makes me a little uncomfortable: how come the solenoid's area is not given, and why is it not relevant to the solution? Shouldn't the flux through the loop depend on the ratio of (area of loop) * cos(37) /(area of solenoid)?

Because inside solenoid, the magnetic field is radially uniform.

I get it. Thanks.

Faraday's Law is a fundamental principle in electromagnetism that describes the relationship between a changing magnetic field and an induced electric field.

## How does Faraday's Law work?

Faraday's Law states that when there is a change in the magnetic flux through a loop of wire, there will be an induced electromotive force (EMF) in the loop. This EMF will cause a current to flow in the loop if it is closed.

## What is the significance of Faraday's Law?

Faraday's Law is significant because it demonstrates the connection between electricity and magnetism and helps explain the behavior of electromagnets and generators.

## Can Faraday's Law be used to generate electricity?

Yes, Faraday's Law is the basis for the operation of electrical generators, which convert mechanical energy into electrical energy by using a changing magnetic field to induce a current in a loop of wire.

## What are some real-world applications of Faraday's Law?

Faraday's Law has many practical applications, including power generation, electric motors, transformers, and electromagnetic induction cooking. It is also used in medical devices such as MRI machines and in wireless charging technology.

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