# Net force between two Electromagnets considering Back EMF

• Student149
In summary, when using two bar electromagnets to simulate bar magnets M1 and M2, placed end to end at distance D apart, the magnets will attract each other and M2 will travel the distance D in some time T1. The net effective force of attraction, taking into account the effects of back EMF, will change with changes in current and voltage. A simple formula for the net force and time taken in relation to changes in these parameters is not available, but it can be calculated using various parameters such as magnetic induction, cross section area of bars, length of bars, mass of M2, magnetic permeability in bars, and characteristic of power supply. It is important to keep in mind the effects of back EMF and
Student149
First this Q might be trivial thus apologies.

Consider two bar electromagnets that can simulate bar magnets M1 and M2, placed end to end at distance D apart (North Pole of M1 facing South Pole of M2). Magnet M1 is 'fixed' to a base. Assuming both electromagnets have the Current I1 and Voltage V1.

The magnets will attract each other and M2 will travel the distance D in some time T1.

How will the the Net effective force of attraction (considering the effects of Back EMF) thus time taken, change with change in:

1. Current
2. Voltage
3. Important: We have to keep in mind the 'Back EMF' generated due to motion, that negates this attractive motion and how it changes with Current and Voltage (the part which I am unsure of).
Q1. Is there a simple formula for the Net Force (and time taken) w.r.t. changes in the above 3.?
Q2. In other words how does changing the parameters, affects the time M2 will take to travel distance D?

The question is not trivial, it is complicated. A lot of information is needed, such as:

- magnetic induction ( B-field ).
- cross section area of bars.
- length of bars
- mass of M2
- magnetic permeability in bars
- characteristic of power supply ( current source / voltage source ).
- impedance in coils

I think that a numerical calculation by computer is necessary, that will do the job within some minutes.

Hesch said:
The question is not trivial, it is complicated. A lot of information is needed, such as:

- magnetic induction ( B-field ).
- cross section area of bars.
- length of bars
- mass of M2
- magnetic permeability in bars
- characteristic of power supply ( current source / voltage source ).
- impedance in coils

I think that a numerical calculation by computer is necessary, that will do the job within some minutes.

Thank you for the reply. I do understand that various parameters are involved. But we can assume the ones like:
- cross section area of bars.
- length of bars
- mass of M2
- magnetic permeability in bars
- characteristic of power supply ( current source / voltage source ).
- impedance in coils

as some random feasible values. The only thing of interest is that how the time taken to travel changes with change in Current and/or voltage. That too, to a reasonable approximation. Something of a graph[Current/Voltage vs Time taken to travel distance D] or a formula to generate it. I have no clue of both, thus needed some help.

B = μ * H = μ0 * μr * H. Say that μr (as for the core) is constant ≈1000. If you multiply the current by a factor k, both B and H will be multiplied by k.

The magnetic energy density, Emagn = ½ * B * H [ J / m3 ], so Emagn will be multiplied by k2.

F = ΔE / ΔV = ΔE / ( A * Δd ), ( E is total magnetic energy, V is the (small) volume of airgap, A is cross section area of airgap, d is distance at any time ), thus also the force will be multiplied by k2.

Now, F = m * a, and d = ½*a*t2 → t = √( 2d / a ), which leads to that time is inverse proportional to k.

Last edited:
Student149
Hesch said:
B = μ * H = μ0 * μr * H. Say that μr (as for the core) is constant ≈1000. If you multiply the current by a factor k, both B and H will be multiplied by k.

The magnetic energy density, Emagn = ½ * B * H [ J / m3 ], so Emagn will be multiplied by k2.

F = ΔE / ΔV = ΔE / ( A * Δd ), ( E is total magnetic energy, V is the (small) volume of airgap, A is cross section area of airgap, d is distance at any time ), thus also the force will be multiplied by k2.

Now, F = m * a, and d = ½*a*t2 → t = √( 2d / a ), which leads to that time is inverse proportional to k.

Thank you for such a clear answer. Much grateful.

Student149 said:
Thank you for such a clear answer. Much grateful.

Hesch said:
B = μ * H = μ0 * μr * H. Say that μr (as for the core) is constant ≈1000. If you multiply the current by a factor k, both B and H will be multiplied by k.

The magnetic energy density, Emagn = ½ * B * H [ J / m3 ], so Emagn will be multiplied by k2.

F = ΔE / ΔV = ΔE / ( A * Δd ), ( E is total magnetic energy, V is the (small) volume of airgap, A is cross section area of airgap, d is distance at any time ), thus also the force will be multiplied by k2.

Now, F = m * a, and d = ½*a*t2 → t = √( 2d / a ), which leads to that time is inverse proportional to k.

Another doubt in the Q. I think we missed the effect of change in Back Emf when increasing the Current by a factor of k (and thus on the change in time taken to travel distance D). This was an important part. Any comments?

Student149 said:
I think we missed the effect of change in Back Emf when increasing the Current

If you use a voltage-source as power supply ( constant voltage output ), then: Yes.

But if you use a current-source as power supply, it automatically compensate this back-emf, and the current will be constant no matter that some back-emf arises.

By a "normal" powersupply you can make it a current-source by:

1) Set the current-limit to some level.
2) Set voltage-output to maximum.

The supply will automatically control the output voltage so that the current will be: Iout = Ilimit.

## What is a net force between two electromagnets?

The net force between two electromagnets refers to the overall force exerted on each other due to their magnetic fields. This force can either be attractive or repulsive, depending on the orientation of the magnets.

## How is the net force between two electromagnets calculated?

The net force between two electromagnets is calculated by taking into account the strength of their individual magnetic fields, the distance between them, and the orientation of their poles. This force can be calculated using the formula F = k * (m1 * m2) / d^2, where k is a constant, m1 and m2 are the strengths of the magnetic fields, and d is the distance between the magnets.

## What is the effect of back EMF on the net force between two electromagnets?

Back EMF, or electromotive force, is an induced voltage that occurs in an electromagnetic system when there is a change in the magnetic field. This can affect the net force between two electromagnets by creating a counteracting force that opposes the original force. This can reduce the overall net force between the magnets.

## How does the distance between two electromagnets affect the net force?

The distance between two electromagnets has a significant impact on the net force between them. As the distance increases, the net force decreases due to the inverse square law. This means that the farther apart the magnets are, the weaker the net force will be between them.

## Can the polarity of the magnets affect the net force between them?

Yes, the polarity of the magnets can greatly affect the net force between them. If the poles of the magnets are opposite (one is north and the other is south), they will exert an attractive force on each other. However, if the poles are the same (both north or both south), they will exert a repulsive force. The orientation of the magnets can also impact the net force between them.

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