Solving the Biot-Savart Problem

[jackdamack10]

I have two questions

1) The problem is here

View of two long, straight and parallel conductors carrying a current as shown below

8 cm
P-------------------------O (I2 = 15 A..out of the page)
l
l 6cm
l
l
O
(I1 = 10A .. into the page)

v = - (3*10^6) K m/s at point P

I must find the net magnetic force it experiences due to the two conductors


I’m not quite sure what to do. This is how I think I should proceed:

-Find the direction of the magnetic fields (B1 and B2). B1 is pointing upwards and B2 is pointing to the left?

-Find B using B = 2KI/distance (for each B1 and B2)

-Find components of B

-F1 = qv X B1 and F2 = qv X B2

Basically, I'm quite unsure about the magnetic field (direction).

 

[quasar987]

You got the steps right and all. But the direction you give for the field is wrong. Maybe you're confused about the right-hand rule. Maybe you don't know about it. It's explained here:

http://mathworld.wolfram.com/Right-HandRule.html

 

[jackdamack10]

well. I don't know u and uXv... Basically, the only value I know of is v. How would I do the right hand rule. Is there a way of finding out about the direction of u simply with I along?\

By the way, is u X v = B?

 

[OlderDan]

well. I don't know u and uXv... Basically, the only value I know of is v. How would I do the right hand rule. Is there a way of finding out about the direction of u simply with I along?\

By the way, is u X v = B?

The u in the diagram is just a general representation of a vector in the diagram showing the right hand rule for cross products. The original comment noted that your field directions are wrong. The right hand rule for a current carrying wire (or a moving charge) is to point your thumb in the direction of positive current. Your fingers then curl around the wire in the direction of the field. The right hand rule illustrated in the diagram then applies to the cross product for finding the force.

 

[jackdamack10]

Thanks, but I just want to make sure i understood:

For the first current, B down. Using RHR, I find that the force is pointing in the negative x direction?

 

[quasar987]

I'm very sorry jackdamack10, I gave you a link to the wrong Right-hand rule. I meant to give you one that explains how to find the direction of the field produced by a curent. The rule goes as follow:

Let your thumb point in the direction of the curent, then curl your other 4 fingers around your thumb (if you hear cracking noises and feel a sharp pain in your hand you're curling in the wrong direction). This is the direction that the magnetic field curls around the wire. Using this rule, you should find that the field produced by I1 at point P is in the direction of positive x.

 

[OlderDan]

Thanks, but I just want to make sure i understood:

For the first current, B down. Using RHR, I find that the force is pointing in the negative x direction?

You have not told us your coordinate system. I cannot tell which way the charge is moving. I can tell the direction of B on the page, but I cannot relate that to x, y, z