What Direction Does the Force on the Wire Point in a Solenoid Setup?

[IHave]

Quick question on force direction...Please help!

Homework Statement

A 550 - turn solenoid is 12 cm long. The current into it is 36 A. A 3.6 cm long straight wire cuts through the center of the solenoid, along the diameter. This wire carries a 26 A current downward (and is connected by other wires that don't concern us).

Part A: What is the force on this wire assuming the solenoid's field points due east?

Part B: to the east; to the north; to the south or to the west

Homework Equations

B = mu(0) * (N/L) * I
F= I * L * B

The Attempt at a Solution

I was able to use the (relevant) equations to find the answer for Part A. It was: F = 0.19 N. However, I'm having trouble figuring out the directions of certain fields. I know there are things like the right hand rule; but I can't seem to conceptualize a 3D visual of how it works; in my head. Please help!

 

[BruceW]

The rule is that for a flow of positive charges, if your index finger points in the direction of current, and if your middle finger points in the direction of magnetic field, then your thumb will give the direction of the force.

It is electrons which flow through a wire, which are negatively charged, so the direction of the force will be made opposite to the rule above (if you're using the true current). But if you use conventional current, then the original rule applies.

In either case, the force will be exactly perpendicular to both the magnetic field and the current.

 

[IHave]

Thanks, I think I have a better grasp on the concept. So for this problem the force points to the south.

 

[BruceW]

Yes, that's right.
Unless specified otherwise, 'current' usually means 'conventional current'. (Which is what I assume they meant in this question).

 

[rwisz]

The force on the wire can be calculated using the equation F= I * L * B, where I is the current, L is the length of the wire, and B is the magnetic field. In this case, we have a solenoid with a current of 36 A and a wire with a current of 26 A. The magnetic field of the solenoid can be calculated using the equation B = mu(0) * (N/L) * I, where mu(0) is the permeability of free space, N is the number of turns in the solenoid, and L is the length of the solenoid. Plugging in the given values, we get B = 0.0002 T.

Now, to determine the direction of the force, we can use the right hand rule. If we point our right thumb in the direction of the current in the wire (downward), and our fingers in the direction of the magnetic field (east), then the force will be in the direction that our palm faces. In this case, the palm faces south, so the force on the wire is to the south.

It's important to keep in mind that the force is always perpendicular to both the current and the magnetic field. In this case, the wire and the solenoid are both oriented along the east-west direction, so the force will be in the north-south direction.

I hope this helps! If you're still having trouble visualizing it, try drawing a diagram or using a 3D modeling tool to help you see the direction of the forces. Practice using the right hand rule with different orientations of current and magnetic field to get a better understanding of how it works.