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.

 

[rwisz]

The magnetic field center of a solenoid can be determined by using the equation B = (mu(0) * N * I) / L, where B is the magnetic field strength, mu(0) is the permeability of free space, N is the number of turns in the solenoid, I is the current flowing through the solenoid, and L is the length of the solenoid. This equation can be used to calculate the magnetic field at any point along the axis of the solenoid, including the center.

Alternatively, the equation B = (mu(0) / 4pi) * ((I * (delta(S) cross r(direction))) / r^2) can also be used, where delta(S) is the surface element, r is the distance from the element to the point of interest, and r(direction) is the direction vector from the element to the point of interest. This equation takes into account the contributions of all the small elements that make up the solenoid to calculate the magnetic field at a specific point.

In order to use these equations, you will need to know the values of the variables, such as the number of turns in the solenoid, the current flowing through it, and the dimensions of the solenoid. Once you have these values, you can plug them into the equations to calculate the magnetic field at the center of the solenoid. It is important to note that both equations assume that the solenoid is infinitely long, so they may not be accurate for solenoids with finite lengths.

In your attempt at a solution, you have correctly identified the variables needed for the equations, but it is important to also consider the dimensions and properties of the solenoid in order to accurately calculate the magnetic field at its center. I would recommend reviewing the given information and understanding the concepts behind the equations before attempting to solve the problem.