Magnetic Field Centre Of A Solenoid

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Homework Help Overview

The discussion revolves around determining the magnetic field at the center of a solenoid, with participants referencing specific equations related to magnetic fields generated by current-carrying conductors. The subject area includes electromagnetism, particularly focusing on solenoids and the application of Ampere's law and the Biot-Savart law.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants express uncertainty about which equations to apply in the context of the problem. There is a discussion about the conditions under which the referenced equations can be used, as well as the meanings of their terms. Some participants attempt to relate the variables a and z to the equations but are unsure of their application.

Discussion Status

The conversation is ongoing, with participants providing insights into the equations and their derivations. Some guidance has been offered regarding the use of the Biot-Savart law and the need to derive the magnetic field for a single loop of wire. However, there is no explicit consensus on the correct approach or resolution of the problem.

Contextual Notes

Participants note that they are working with equations that may not directly apply to the problem at hand. There is mention of missing information regarding the variable delta(S) and its significance in the context of the Biot-Savart law.

abdullahkiran
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Homework Statement


[PLAIN]http://i27.lulzimg.com/ac8f155fa0.jpg

[PLAIN]http://i27.lulzimg.com/b5f4ac2fce.jpg

Homework Equations



1. B = ((mu(0) * N * I )) / L ,, 2. (mu(0) / 4pi)*((I*(delta(S) cross r(direction)))/r^2)



The Attempt at a Solution



im not really sure which equations to use. i tried to input the variables a and z into the second equation, but I am sure if it is correct or not.
 
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abdullahkiran said:
1. B = ((mu(0) * N * I )) / L ,, 2. (mu(0) / 4pi)*((I*(delta(S) cross r(direction)))/r^2)
First of all, what are these equations used for? Under what conditions can they used and what do the terms mean?
 
i know that equation 1. amperes law i think , is used for solenoids with no core
and the second is for a segment of current wire.

i picked these 2 because it seemed like they would satisfy the terms that was required in the answer. except i still don't know where i could include variables a and z :S

these i have covered:
mu (constant), N = number of turns , I = current , L = length , r = radius of solenoid ,

except delta(S) = i actually don't know lol.
 
Yes, equation 1 is the equation for a solenoid with no core. It can be derived using Ampere's law. But it's not the Ampere's law.

Equation 2 is the Biot-Savart law. You can refer http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law" and compare to find out what the vector delta(S) is.

Neither of these equations can be used directly here. Looks like what you need is the magnetic field on the axis of the single loop of a current carrying wire, at a distance z form it's center.

If you were not given that equation in class, or if it is not in your textbook, you can derive it using the Biot-Savart law (equation 2).

You just have to take delta(S) to be a small element of the wire, find the magnetic field z distance away from the center along the axis using the Biot-Savart law, and integrate over the whole loop.
 
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