How Do Magnetic Fields and Forces Behave Around Infinite Wires?

[Hooke's Law]

Homework Statement

Two infinitely long wires run parallel to the z-axis. Wire a is 5.0 cm along the y-direction from the z-axis and carries a current of 1.5 A out of the page. Wire b is 10.0 cm long along the x-direction from the z-axis carries a current of 0.5 A into the page.

a) calculate the magnetic field at a point on the z-axis. Express your answer in unit vector notation.

b) What would be the direction of the force on a positive charge moving out of the page along the z-axis. Give your answer as an angle measured from the positive y-axis.



r1 = 0.05 m
r2 = 0.1 m
I1 = 1.5 A ( out of the page )
I2 = 0.5 A ( into the page )

Homework Equations

B =( mu * I ) / ( 2*Pi*R )

F = q ( v x B )

The Attempt at a Solution

a ) Bz = B1 + B2
= mu/2*Pi [ (- I1/ r1 ) ( -0.05 j ) + ( I2 / r2 ) ( -0.1 i ) ]
= (9.42*10^-7j - 3.14*10^-7i ) T

Is my calculations right ? I'm not sure if there's a z component, but I first thought that there will be a -z and +z from the current directions. I placed I1 with a -ve sign because it's going into the page.



b) Since there the charge is moving in the z-axis ( k ), the direction of the force is in the +i direction and -j direction . I'm not sure if I did the right answer in a) to solve for b).

Thanks

 

[cupid.callin]

a ) Bz = B1 + B2
= mu/2*Pi [ (- I1/ r1 ) ( -0.05 j ) + ( I2 / r2 ) ( -0.1 i ) ]
= (9.42*10^-7j - 3.14*10^-7i ) T

Due to wire1 field won't be in -Y axis
it will be in +X axis

here's how to find the direction of field:
[URL]http://flightline.highline.edu/iglozman/classes/physnotes/media/magstraight.gif[/URL]

and also correct for wire2

and why have you written r1 and .05 separately?
r1=.05 and it will be in denominator.

 

[Hooke's Law]

Due to wire1 field won't be in -Y axis
it will be in +X axis

here's how to find the direction of field:
[URL]http://flightline.highline.edu/iglozman/classes/physnotes/media/magstraight.gif[/URL]

and also correct for wire2

and why have you written r1 and .05 separately?
r1=.05 and it will be in denominator.

r1 is the distance r, and 0.05 is the vector in y-direction. They both have the same values.
I tried the diagram that you showed me, and I get wire A in -y direction, while wire B will be +X direction. I'm not sure if I'm doing my right hand right with the diagram because of the rotating magnetic field which could either be in X or Y direction..could you please explain how? Or with the curl, how do you know the direction of the magnetic field (if it is in X or Y direction)?

Thanks

 

[Hooke's Law]

and why have you written r1 and .05 separately?
r1=.05 and it will be in denominator.

Should there be values for i ( hat ) and j ( hat )?