# Electromagnetic damping logarithmic decrement task

• wetback
In summary: This term is proportional to Λ, which is the damping term. Maybe you're wondering about the sensitivity of the damping to changes in the size or shape of the inductor.
wetback

## Homework Statement

The contour consists of a condenser with capacitance C = 2.22*10^-9 F and a coil of copper wire. The diameter of the wire 5*10^-4 m, the length of the coil 20*10^-2 m. Determine the damping logarithmic decrement Λ of the fluctuations?

## Homework Equations

damping logarithmic decrement: Λ=2*Pi/sqrt((4L/CR^2)-1)
self-inductance of a coil: L=4*Pi*10^-7*(N^2/lc)*Sc (N number of turns, lc length of coil, Sc area of coil section)
resistance of the coil: R=(ρCu*lw)/(Pi*(d/2)^2) (ρCu=1.7*10^-8, lw-length of the wire,d-diameter of the wire)

## The Attempt at a Solution

The answer I got by combining the three equations: ~2.79*10^-12 . Probably wrong because differs a lot from the given so I'm asking for help.

Is the "length of the coil" the actual length of the wire used to make the inductor (i.e. if you unwrapped the whole thing), or is it the length measured across the outside of the coil? If it's the former, how many coils are there? If it's the latter, what is the cross-sectional area of the coil? Information is missing.

tman12321 said:
Is the "length of the coil" the actual length of the wire used to make the inductor (i.e. if you unwrapped the whole thing), or is it the length measured across the outside of the coil? If it's the former, how many coils are there? If it's the latter, what is the cross-sectional area of the coil? Information is missing.

Length of the coil is the length of the cylinder shape the coil makes. There is no information missing. You are supposed to use equations to eliminate the need for the missing information. The task is from a widely used book.

wetback said:
Length of the coil is the length of the cylinder shape the coil makes. There is no information missing. You are supposed to use equations to eliminate the need for the missing information. The task is from a widely used book.

Maybe I'm misunderstanding something. You know the length of the coil. You know the diameter of the wire. So you know the number of turns. But you don't know the total length of the wire, so you can't figure out the circumference of a single loop or its cross-sectional area. It could be anything and still satisfy the length of the coil and the number of turns. I don't believe you supplied this information.

Not sure what is meant by "damping logarithmic decrement". The exponential term is R/2L, i.e. the envelope decays as exp(-Rt/2L).

## What is electromagnetic damping?

Electromagnetic damping is a type of damping that occurs when an electrical current is induced in a conductor placed in a magnetic field. This current creates a force that opposes the motion of the conductor, resulting in the dissipation of energy and thus reducing the amplitude of oscillations.

## What is logarithmic decrement?

Logarithmic decrement is a measure of the rate of decay of a damped oscillation. It is calculated by taking the natural logarithm of the ratio of the amplitude of two consecutive oscillations. It is often used to quantify the damping effect in systems, such as electromagnetic damping.

## How is electromagnetic damping logarithmic decrement calculated?

The electromagnetic damping logarithmic decrement can be calculated by using the equation: δ = ln(An/An+1), where δ is the logarithmic decrement, An is the amplitude of the nth oscillation, and An+1 is the amplitude of the (n+1)th oscillation.

## What factors affect the electromagnetic damping logarithmic decrement?

The electromagnetic damping logarithmic decrement can be affected by several factors, including the strength of the magnetic field, the electrical conductivity of the conductor, and the frequency of the oscillations. In general, a stronger magnetic field and a higher electrical conductivity will result in a higher logarithmic decrement.

## What are some real-world applications of electromagnetic damping logarithmic decrement?

Electromagnetic damping logarithmic decrement has various applications in engineering and physics, such as in electrical motors, shock absorbers, and various measuring devices. It is also used in earthquake engineering to dampen the vibrations of buildings and structures.

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