Physics tpr mcat passage help!!!!!

[crazy person]

I need some help with a passage (Magnetism) from the TPR physics book. On page 332, question 6, I'm having trouble understanding why the answer is C. I don't get why on the back of the book it says for wire A and wire B have the same current when wire A is going to the right and wire B is going to the left so wouldn't they have different currents?
Also, in between the currents, for path 2 it says that the magnetic field is going into the page but for path 2: isn't the magnetic field for wire A going inside the page and for wire B: the magnetic field is going out of the page. I'm sooo confused. Can someone please explain it to me??????

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[contraband]

They state that the magnitude of the current is the same in each wire, with opposite direction (which I think answers your first point of confusion; current is a scalar anyway).

For the next point, use the right hand rule for wire A - below wire A your fingers will be pointing down towards the paper with your thumb pointed to the right. For wire B, your thumb is pointed left, meaning that above wire B, your fingers will also be pointing down into the page.

 

[crazy person]

ok I get that part now. But when I'm finding the force for path 2 (wire A and wire B), from wire A I'm getting the direction up ( i am using RHR and flipping it since its an electron) and when I'm finding the force from wire B, I'm getting the direction down (using the RHR). So I know I'm doing something wrong. Well, first of all, I thought the magnetic fields cancel out since they're both inside the page for wire A and B. If not then, which wire do we use to find the force for path 2 because the marble is close to both wire A and B??????

Another question that its bothering me its comparing question 2 and 6. For question 2, I get that the force is zero because wire A is equal in magnitude and opposite in direction from the magnetic field created from wire B. So, can't we applied the same concept for question 6 as well, meaning that for path 1 and 3, the magnetic fields generated by each wire are equal in magnitude but in opposite directions, therefore the force will also be zero??????

 

[contraband]

Remember that there are really two right hand rules:
Rule 1: Direction of a magnetic force given the direction of the magnetic field and the direction of the velocity: L hand for negative charge, R hand for positive charge, thumb along v, fingers along B, push for the direction of the force
Rule 2: Direction of a magnetic field given the direction of a moving charged particle: again L hand for negative charge, R hand for positive charge (which includes current, since current is the direction that positive charge carriers WOULD travel). Thumb in the direction of v of the charged particle(s), and you curl your fingers to find the direction of B. Notice that if you point your L thumb in the direction that electrons go and your R thumb in the direction the current goes (they are opposite), that the curling of your fingers goes the same direction.

In questions like this it's important to apply these rules in a stepwise fashion. To determine the direction of the magnetic force, you MUST first determine the direction of the magnetic field, so use RHR2 first to find the direction of B, then use RHR1 to find the direction of the magnetic force. In this case, the B-field from both wires will point into the plane of the page between both wires, meaning that the overall B-field points into the page. THEN apply RHR1 to find the direction of the force. It's a negatively-charged moving object, so point your left thumb to the right and your fingers into the plane of the page. You'd push down with your palm, meaning that the force is downward.

As far as your second question
Remember that for Fm = q x v x B, the strength of the magnetic force is proportional to the strength of the magnetic field. Equation 1 in the passage tells us that the strength of the magnetic field from a wire is inversely proportional to the distance from the wire. Thus, for path 1, the magnetic field from A will be stronger than the magnetic field from B, meaning that the net magnetic field will be pointing OUT of the plane of the page. Similar explanation for path 3.

Hope this helps, let me know if you need further explanation.

 

[crazy person]

OMG !!!! THANK YOU !!!
I almost gave up but thanks to your explanation I finally understand it now! You are AWESOME !!!
=)

 

[contraband]

No problem! Let me know if you have other questions.