# Electromechanical energy conversion problem

• Engineering
• cnh1995
In summary: The summary is as follows:In summary, the force applied on the moving part at t=0+ will be the derivative of field energy w.r.t displacement of the moving part, with constant current. Using this insight, I got F to be 141.4 N.
cnh1995
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Homework Statement
The problem statement is as follows:
Relevant Equations
Energy stored in a magnetic circuit=

Force on a movable part in the magnetic circuit=
F= -dE/dx.

Here, I have assumed very quick movement of the moving part. So, as per the mmf-flux curve, flux linking with the system will be unchanged during the movement. To support this assumption, I have made use of the following analysis.

In this graph, the movement of the part happens quickly (small air gap), hence, the the flux linkage will remain unchanged (line PQ) throughout this small interval.

I hope I have sufficiently presented my attempt at a solution. Sorry for the messy white-board though.

The answer I got is F=282.4N but the answer according to the official answer key is 188N.

Where did I go wrong here? Any help is appreciated.

It looks like some information is missing in this problem, IMO. A 10cm air gap is giant, unless the cross-sectional area of the magnetic core is also huge. What are the rest of the dimensions for this system? What are the dimensions of the metal piece in the air gap? Is it magnetized?

If it's not magnetized, then it will be the non-uniformity of the flux in the air gap that will attract the moving metal piece to one of the core surfaces at the air gap (whichever is closer when the metal piece is released), no?

https://www.etcourse.com/news-blog/air-gap-in-magnetic-circuits

cnh1995

The force applied on the moving part at t=0+ here will be simply the derivative of field energy w.r.t displacement of the moving part, with constant current.
Using this insight, I got F to be 141.4 N.
I will post my work in some time.

Now I doubt if the official answer key is correct.

## What is Electromechanical Energy Conversion?

Electromechanical energy conversion is the process of converting electrical energy into mechanical energy, or vice versa. This involves the use of devices such as motors, generators, and transformers.

## What are the main principles behind Electromechanical Energy Conversion?

The main principles behind electromechanical energy conversion are Faraday's law of electromagnetic induction, Lenz's law, and the conservation of energy. These principles explain how electrical energy can be converted into mechanical energy and vice versa.

## What are the common types of Electromechanical Energy Conversion devices?

The common types of electromechanical energy conversion devices include motors, generators, transformers, and electromagnets. Each of these devices plays a specific role in converting energy between electrical and mechanical forms.

## What are the key factors that affect Electromechanical Energy Conversion?

The key factors that affect electromechanical energy conversion include the type of material used, the design of the device, the amount of electrical energy input, and the efficiency of the conversion process. Other factors may also include temperature, magnetic field strength, and mechanical load.

## What are some real-world applications of Electromechanical Energy Conversion?

Electromechanical energy conversion has numerous real-world applications, including in electric vehicles, industrial machinery, renewable energy systems, and household appliances. It is also used in medical devices, such as MRI machines, and in aerospace technology, such as satellites and spacecraft.

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