Find Magnetic Field of Infinitely Long Line Current

[musiliu]

Homework Statement

Homework Equations

B = u0 I / 2 pi r (perpendicular)

The Attempt at a Solution

This seems like a simple plug in values equation, but the 3-dimensions is confusing me, and I can't figure out what the value of r(perpendicular) should be, and what the direction should be..

I can't seem to draw the r(perpendicular) to the line current..since it's 3d, if i try to make it perpendicular i end up with a point above the x-axis and i don't think the line current is in the z plane..

Need help please, thanks.

 

[Xerxes1986]

Try to draw it on a piece of paper...you will see that because the infinite line is along the x-axis, the distance from the line aka the distance from the x-axis doesn't depend on x at all. Only y and z. Then you can see that if you move up 1 in the y direction and 1 in the z direction you have a right triangle with sides 1 and 1 whose hypotenuse is r = sqrt(2). Using this value you can calculate the magnitude and the direction is given by the right hand rule

 

[musiliu]

oh...i always thought r(perpendicular) meant draw a line connecting the current to the point of interest and angle was always 90 degrees, i didn't know i could do that for r
edit: i don't understand how r= sqrt(2) can be perpendicular to the line current.. r seems like a diagonal line ..

for the right hand rule, i could never do it right...i don't know how to position my hand according to the current..which direction do i curl my fingers?
is the direction in the positive z direction?

 

[musiliu]

ok, i understand the r perpendicular value now, but can someone explain in detail what they do to find the direction using right hand rule?

is the direction counterclockwise in y-z plane and in x-y plane the direction is in both +z and -y direction?

 

[Xerxes1986]

ok, i understand the r perpendicular value now, but can someone explain in detail what they do to find the direction using right hand rule?

is the direction counterclockwise in y-z plane and in x-y plane the direction is in both +z and -y direction?

You know the magnetic fields go either clockwise or counterclockwise around the wire. To find the direction, imagine the thumb of your right hand points in the direction of the current, then your fingers will curl in only one direction and that is the direction of the magnetic field.

And btw, http://tinyurl.com/2u9glqh" ;)

 

[musiliu]

ok, but what would you say is the direction for this problem? I'm supposed to find the direction at that point (1,1,1).. so i don't think I'm just supposed to put the entire direction of the magnetic field.. is the direction at that point in the +z and -y direction?