# Induced Current Problem from the professor not in our textbook

• stevencarlover
In summary, the question poses a scenario involving a solenoid with certain specifications, a small ring with a set resistance placed at the center of the solenoid, and a change in current over time. The task is to find the direction and magnitude of the current induced in the ring during this period. The formulas for mutual inductance and induced emf are provided, but the lack of values for N1, N2, and L makes it difficult to solve for the mutual inductance and, subsequently, the induced current in the ring. However, if the solenoid flux is independent of the ring current, then the formula for emf can be used without considering the second term. It is also suggested to follow the suggestion
stevencarlover

## Homework Statement

A long straight solenoid of cross-sectional area 400 cm^2 is wound with 10 turns of wire per centimeter, and the winding carry a current in the direction shown (downward). A small ring of radius 5.00 cm and resistance 0.300 ohms is placed at the center of the solenoid. If the current in the solenoid increases from 20.0 Amps to 60.0 Amps in 2.50 seconds, find the direction and magnitude of the current induced in the ring during this period.

## Homework Equations

M = (Mu0)(A)(N1)(N2)/L
emf = M(di/dt)
emf = I *R

## The Attempt at a Solution

Since the question does not give values for N1, N2, and L I do not know how to find the mutual inductance and thus the induced current in the ring.

If you know the current through the solenoid, can you find the magnetic flux passing through the ring?

stevencarlover said:
M = (Mu0)(A)(N1)(N2)/L
emf = M(di/dt)
emf = I *R
Since the question does not give values for N1, N2, and L I do not know how to find the mutual inductance and thus the induced current in the ring.
Your formula assumes no flux coupled into the solenoid from the ring, i.e. ring current is assumed small (Lring Iring << M Isolenoid to be precise. Strictly speaking your ring emf = M(di/dt) - Lring(diring/dt). But you have the right formula for emf since computing the second term is exceedingly difficult. I mention it only for the record.

In which case the question does give N1, N2 and l (your L should be rewritten l to diIstinguish it from inductance). All you need do is find A.

Or, better, follow cnh1995's suggestion, again assuming the solenoid flux is independent of the ring current.

cnh1995

## 1. What is an induced current problem?

An induced current problem is a type of physics problem that involves calculating the direction and magnitude of an induced current in a circuit. This type of problem typically involves a changing magnetic field and the use of Faraday's Law of Induction to solve.

## 2. How is an induced current problem different from other physics problems?

Induced current problems are unique in that they require the use of Faraday's Law of Induction, which states that a changing magnetic field will induce an electric current in a nearby conductor. This makes these problems more complex and requires an understanding of both electromagnetism and circuit analysis.

## 3. What are some common mistakes to avoid when solving an induced current problem?

Some common mistakes in solving an induced current problem include forgetting to take into account the direction of the induced current, not correctly applying Faraday's Law, and not considering the effects of resistance in the circuit. It is important to carefully analyze the given information and use all relevant equations to solve the problem accurately.

## 4. How can I prepare for solving induced current problems on exams?

To prepare for solving induced current problems on exams, it is important to practice solving similar problems beforehand. This will help you become familiar with the necessary equations and techniques. It is also helpful to review the concepts of electromagnetism and circuit analysis to ensure a strong foundation in the subject.

## 5. Are there any real-world applications of induced current problems?

Yes, there are many real-world applications of induced current problems. Some examples include generators, transformers, and magnetic braking systems. These applications utilize induced currents to produce electricity, transfer energy, and slow down moving objects. Understanding induced current problems is crucial in the design and operation of these technologies.

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