# Induction of a coil and force exerted on magnet in a magnetic field

• Detektyw
In summary, the individual has a high school level of math knowledge with some basic calculus and limited physics skills in electromagnetism. They are seeking help with two problems: a) calculating the magnetic induction of a copper coil with an electricity source attached, and b) calculating the force exerted on a permanent magnet in a symmetrical coil with a current flowing through it. The individual has found a solution for the first problem and is open to corrections.
Detektyw
Hi! This is my first post on this forum, and I have two questions.

First of all I'd like to mentoin that my math knowledge is at high school level + some basic calculus. Ah, and I haven't learned about (partial) differential equations yet.

My physics skills go only as far as electromagnetism and so if someone answered this question I would be really grateful for any explanations of the phenomena or algebra above the level described.

My problems are:

a) How to calculate magnetic induction (scalar) of a copper coil with an electricity source attached without a core (if someone knows how to calculate it with a core I'd like to know that too, but it's not necessary for what I'm doing now) ?

b) How to calculate the force exerted on a permanent magnet in such a coil if we assume that the coil is symmetrical and there is a current flowing through it. The preferred form would be as a function of distance from the center of the coil.

Last edited:
Update:

I've found the solution for the simpler version of the first problem.

H = N * I/L where N is number of windings (dimensionless), I the current (amps), L the length of the coil's wire (meters).

H times permability of the magnet is the induction.

If I've mistaken somewhere, please correct me.

To answer your first question, the magnetic induction (also known as magnetic flux density or magnetic field strength) of a coil can be calculated using the equation B = μ₀N/l, where B is the magnetic induction, μ₀ is the permeability of free space (a constant value of 4π x 10^-7 N/A^2), N is the number of turns in the coil, and l is the length of the coil. This equation assumes that the coil has a uniform cross-sectional area and is wound tightly without any gaps.

If you want to calculate the magnetic induction with a core, you can use the equation B = μ₀μ_rN/l, where μ_r is the relative permeability of the core material. This value can vary depending on the material used for the core.

For your second question, the force exerted on a permanent magnet in a coil can be calculated using the equation F = BIl, where F is the force, B is the magnetic induction, I is the current flowing through the coil, and l is the length of the coil. This equation assumes that the coil is perpendicular to the magnetic field produced by the magnet.

To calculate the force as a function of distance from the center of the coil, you will need to use the equation F = (μ₀NIl)/2r, where r is the distance from the center of the coil and the other variables have the same meaning as before. This equation takes into account the fact that the force exerted by the coil decreases as the distance from the center increases.

I hope this helps answer your questions and provides a starting point for your further exploration of electromagnetism. Keep learning and asking questions!

## 1. How does induction of a coil work?

The process of induction of a coil involves moving a magnet inside or near a coil of wire, which creates a changing magnetic field. This changing magnetic field induces an electric current in the coil, according to Faraday's law of induction. This current can then be used to power devices or perform other tasks.

## 2. What factors affect the strength of the induced current?

The strength of the induced current depends on several factors, including the strength of the magnetic field, the speed at which the magnet is moved, the number of turns in the coil, and the resistance of the coil. Generally, a stronger magnetic field, faster movement, more turns, and lower resistance will result in a stronger induced current.

## 3. What is the direction of the induced current in a coil?

The direction of the induced current in a coil is determined by Lenz's law, which states that the direction of the current is always such that it opposes the change in the magnetic field that induced it. This means that the induced current will flow in a direction that creates a magnetic field that cancels out or opposes the original changing magnetic field.

## 4. How is the force exerted on a magnet in a magnetic field calculated?

The force exerted on a magnet in a magnetic field is calculated using the formula F = BIL, where B is the strength of the magnetic field, I is the current in the wire, and L is the length of the wire in the magnetic field. This is known as the Lorentz force law and is used to calculate the force on a magnet in a variety of situations.

## 5. What are some practical applications of induction of a coil and the force exerted on a magnet in a magnetic field?

The principles of induction and magnetism have many real-world applications, such as powering generators in power plants, creating electric motors, and even in everyday items like speakers and headphones. They are also used in medical devices, such as MRI machines, and in transportation technology, such as maglev trains.

• Electromagnetism
Replies
6
Views
474
• Electromagnetism
Replies
5
Views
1K
• Electromagnetism
Replies
4
Views
1K
• Electromagnetism
Replies
43
Views
2K
• Electromagnetism
Replies
21
Views
1K
• Electromagnetism
Replies
21
Views
2K
• Electromagnetism
Replies
4
Views
1K
• Electromagnetism
Replies
16
Views
2K
• Electromagnetism
Replies
13
Views
2K
• Electromagnetism
Replies
12
Views
1K