Electromagnetism question -- Forces between two current carrying wires

[cutielollipop]

Homework Statement

State whether the magnetic fields around each wire are clockwise or counter-clockwise. Will the wires repel or attract each other

Relevant Equations

right-hand rule

Here is the question. I just wanted to confirm and see if I'm understanding the question clearly. For 3a) I said the first wire would have the magnetic field going in a counter clock wise direction and the second wire would have a magnetic field going in a clockwise direction using the right hand rule. However I don't know if the wires will repel or attract each other. I think they will repel since the magnetic fields are in opposite directions. Help would be kindly appreciated.

For b) I said there would be an upward force on the wire.

Thanks for your help.

 

[berkeman]

You are correct about the B-field directions for the wires. For the forces, have you learned the vector Lorentz Force yet? That's the easiest way to develop the intuition about the resulting forces between current carrying wires.

 

[cutielollipop]

I learned about Lenz's Law if that's what you mean. But I don't know about the vector Lorentz Force.

 

[berkeman]

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html

The magnetic field from one wire interacts with the moving electrons in the other wire to cause the force (attractive or repulsive) between the wires.

Edit -- Remember that the charge $q$ of an electron is negative, since that affects the direction of the Lorentz Force on the moving charge.

 

[haruspex]

I find it easiest to visualise the behaviour, which I do by thinking of the field lines as trying to broaden, repelling their neighbours, and to shrink in length.
If both sets are clockwise, they will cancel in the middle and the two sets connect up. You end up with a single set of field lines clockwise around both. Their shrinking in length will pull the wires together.
If one set is clockwise and the other anticlockwise they will be parallel and in the same direction in the middle. Broadening them pushes the wires apart.

 

[hutchphd]

Edit -- Remember that the charge q of an electron is negative, since that affects the direction of the Lorentz Force on the moving charge.

With respect, this is an inopportune moment to worry about this. Positive currents and fictitious positive carriers get you where you want to go IMHO.

Also if you have two wires do not use your left hand for one and your right hand for the other. Do not inquire as to why I mention this.

 

[berkeman]

With respect, this is an inopportune moment to worry about this. Positive currents and fictitious positive carriers get you where you want to go IMHO.

But, but, my brain doesn't work that way. Makes me dizzy to try to do that...

Also if you have two wires do not use your left hand for one and your right hand for the other. Do not inquire as to why I mention this.

 

[kuruman]

I find it easiest to visualise the behaviour, which I do by thinking of the field lines as trying to broaden, repelling their neighbours, and to shrink in length.
If both sets are clockwise, they will cancel in the middle and the two sets connect up. You end up with a single set of field lines clockwise around both. Their shrinking in length will pull the wires together.
If one set is clockwise and the other anticlockwise they will be parallel and in the same direction in the middle. Broadening them pushes the wires apart.

I have already memorized "same sign charges repel, opposite sign charges attract." If I want to bypass the right hand rule and $~\mathbf{F}=I\mathbf{L}\times\mathbf{B}~$, I find it easier to memorize and use the rule "parallel currents do the opposite from charges, same direction attract, opposite direction repel."

I have seen students during tests writing with their right hand while using their left hand to figure out magnetic field directions, presumably to save time. Left-handed students have a definite advantage here.