Magnetic Fields of Long Straight Wires

[nhartung]

Homework Statement

Two long straight wires are shown. Wire 1 has a current of 25A and lies 0.05 m away from point O. Wire 2 carries a current of 110 A and sits a distance of 0.25m away from point O as shown.

(i) What is the direction and magnitude of the magnetic field at point O due ONLY to WIRE 1.

(ii) What is the direction (measured as an angle from the x-axis) of the magnetic field at point O from wire 2?

(iii) What is the magnitude of the magnetic field at point O due ONLY to WIRE 2?

(iv) What is the magnitude of the total magnetic field?

Homework Equations

B = (4pix10^-7)I/(2pi*r)

The Attempt at a Solution

(i) Using the equation for a long straight wire I get B = 1.0 x 10^-4 I'm a little confused on the direction. I'm not sure how to compute this. Do I need to use the right hand rule or is there some way to find an exact angle?

(ii) As in (i) I am confused on how to find this. I would guess 40 degrees.

(iii) Using the equation for a long straight wire i get B = 8.8 x 10^-5

(iv) Here I'm assuming I need to use the angle I found above to figure this out.

 

[Saraphim]

Recall the right hand rule. A current will create a magnetic field that curls in the direction of your curled fingers when you grasp the wire with your thumb going in the direction of the current. Wire 1 lies on the x axis. In which direction does the magnetic field point in point O?

 

[nhartung]

I don't really understand the right hand rule for long straight wires. When I try it I get the current is into the page which gives B down or in the -y direction. But I also get the same direction for current out of the page. Unless we are talking about clockwise or counterclockwise? In that case (i) would be clockwise.

 

[Saraphim]

Grasping wire one so that your thumb goes in the direction of the current means that your thumb is pointing into the screen. The current in wire two goes in the opposite direction (ie your thumb is now pointing at your face from the screen. :-))

 

[Saraphim]

You are also correct that both directions are down. At least down-ish. The first one is straight down, as it lies on the x-axis, so the tangent to the field at point 0 is vertical. But what about the second one?

 

[nhartung]

Would it be 50 degress with respect to the x-axis? I'm assuming this because if wire 2 were on the x-axis as in wire 1 it would also be vertical but instead it is 40 degrees from the x-axis meaning that the B is perpendicular to wire 2 making it 50 degress from the x-axis.

 

[Saraphim]

I think you are on the right track. I would call it minus 50 degrees though. The field lies in the direction perpendicular to the distance from the wire (or perhaps more clearly, tangential to the circle described by the field line.) Therefore, perpendicular to the 40 degrees, and from the right hand rule, in the negative direction. 40-90=-50.

 

[nhartung]

Ok so I think that covers (i) - (iii). Now for (iv) I'm thinking I need to find the magnitude of the magnetic field by separating each magnitude into its x and y components add them and then do sqrt(B_x² + B_y²).

Is this correct?

 

[Saraphim]

Yes it is. :)

 

[nhartung]

Ok thanks a lot for your quick replies. :D

 

[Saraphim]

Very welcome. If you bump into similar problems, try taking the time to draw the field lines at and near the point where you want to know something. Usually this will help a lot in visualizing the solution. :)