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 )?

 

[rwisz]

for any help!

Your calculations for the magnetic field at a point on the z-axis are correct. There is no z-component because both wires are parallel to the z-axis, so the only components are in the x and y directions.

For part b), you are correct that the direction of the force on a positive charge moving out of the page along the z-axis would be in the +i direction and -j direction. However, to find the angle from the positive y-axis, you can use the right-hand rule. Point your fingers in the direction of the current (out of the page for wire a and into the page for wire b) and your thumb in the direction of the velocity (out of the page for the charge). The direction your palm is facing is the direction of the force, and the angle from the positive y-axis can be found using trigonometry.