Magnetic Field Centre Of A Solenoid

[abdullahkiran]

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.

 

[omoplata]

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?

 

[abdullahkiran]

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.

 

[omoplata]

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.