How Do You Calculate the Magnetic Field Near a Solenoid?

[SamL]

Homework Statement

A pair of wires carry a current I=2.4 A to and from a solenoid. The solenoid contains 600 coils of wire wrapped in a cylinder 15 cm long and 1 cm in diameter.
a.) What is the magnitude and direction of the magnetic field at point A d1= 5 mm from the near wire and d2= 7 mm from the far wire?

Homework Equations

B=(m0*N*I)/l

The Attempt at a Solution

We know m0, N, and I but I'm not sure if the length is supposed to be the 5 mm or 15 cm? Obviously which ever I use I'll have to convert to meters. Do I just plug that stuff into the equation above and I'll have the answer? After I find the magnetic field magnitude with the equation, I'll use the right hand rule to find out which direction it points.

 

[gneill]

The length will be the length of the solenoid; the field depends upon the number of turns per unit length.

It's not clear from your problem statement exactly where the points in question are located with respect to the solenoid: So many millimeters away from a wire could be in any direction. How are we to know what is the "near wire" and the "far wire"? Also, the field direction is going to depend upon the current direction and the sense of the winding. Was a diagram included with the problem?

 

[SamL]

Yes it was. I thought I posted it already. Sorry, here it is

 

[davenn]

this is easier to view without having to open pesky pdf files ...

 

[gneill]

So it looks like point A might be nowhere near the solenoid; the distance of point A from the solenoid is not given. It is, however very near the two wires. Does that suggest anything to you?

 

[SamL]

So if it's nowhere near the solenoid, I don't use the solenoid equation, B=(m0NI)/l? Is that what you're saying? Would I use B=(m0/2pi)(I/d) since the wires are in parallel right there and not all twisted up like a solenoid? The d value would be either d1 or d2, depending upon which I chose to do first, and the I value would 2.4 A. Is that correct?

 

[lep11]

Would I use B=(m0/2pi)(I/d) since the wires are in parallel right there and not all twisted up like a solenoid? The d value would be either d1 or d2, depending upon which I chose to do first, and the I value would 2.4 A. Is that correct?

Yes it is. And the magnetic field at point A is superposition of the two magnetic fields.

 

[gneill]

So if it's nowhere near the solenoid, I don't use the solenoid equation, B=(m0NI)/l? Is that what you're saying? Would I use B=(m0/2pi)(I/d) since the wires are in parallel right there and not all twisted up like a solenoid? The d value would be either d1 or d2, depending upon which I chose to do first, and the I value would 2.4 A. Is that correct?

That's the idea.

By the way, you can access Greek letters and other symbols via the $\Sigma$ icon in the edit panel, in case you want to write μ_o rather than m0.

 

[SamL]

Awesome thanks! :)