Force between two long parallel current carrying conductors

[logearav]

Homework Statement

Revered members,
please see my attachment

Homework Equations

AB and CD are two straight very long parallel conductors placed in air at a distance a. They carry currents I1 and I2 respectively. B1 and B2 are magnetic inductions.
In the book its been mentioned the direction of force can be found out using Fleming's left hand rule.

The Attempt at a Solution

Flemings left hand rule states, stretch the first three fingers of left hand mutually perpendicular to each other, if forefinger represents the direction of magnetic field, middle finger represents the direction of current, then the thumb represents the direction of force.
I have attempted to find the direction of force using this rule. In my attachment i have drawn two right angled line, on the left of AB and to the right of CD. MF represents middle finger and FF represents forefinger.
so my left hand's middle finger is pointing to the direction of current, so according to the left hand rule, the force should point upwards, that is upwards where the two lines meet that is where forefinger line and middle finger line intersect . But here the direction of force is different, also direction of magnetic field is different.
So where do i go wrong? Please let me know members
Thanks in advance

 

[Bob at PC]

In your diagram, "ff" should be pointing "out" of diagram towards you. It hurt to put my fingers in those directions :-)

 

[logearav]

Thanks for the reply BoB. But my question is if my middle finger points in the direction of current, other fingers should point the direction of magnetic field and force. Why am i not getting it?

 

[Bob at PC]

In your diagram, "mf" is in the direction if I1. So far - so good.

"ff" should be in the direction of the magnetic field produced by I2 - which is OUT of the page at the position you have your fingers in your sketch. You draw it pointing to the left.

If you redraw "ff" so it points out of the page, you will then find that your thumb is pointing to the right - directly at wire 2.

You really have to twist your hand so "ff" is pointing straight at you.

 

[logearav]

Ok, understood 80 % sir. But how can i predict the magnetic field's direction. Coz i know only the direction of flow of current. Is there any way to find the direction of magnetic field. Again Thanks a lot for your reply

 

[Bob at PC]

There are two ways you might try:

1) The right hand rule - Hold your right hand as you might if you were hitching a ride. Your thumb is extended and your fingers curl around your palm. Place your lthumb along the direction of current I2. Its magnetic field will resemble your curled fingers. Notice they come out of the page on the left of I2 and into the page on the right of I2.

2) Cross product - calculate I X r. Here, I is the current I2 creating the magnetic field at I1, and r is a vector from the wire carrying the current I2 to the position where you had "ff' and "mf" in your diagram. That is, r points to the left (left from wire 2).

I X r will be out of the page - that is the direction of the magnetic field from I2 in the vicinity of I1.

 

[logearav]

Thanks Mr. Bob. I got it now