Force between two current carrying wires

[Shivansh Mathur]

I've learned how to know the direction of force on a current carrying conductor when placed in a magnetic field.( Fleming's left hand rule)

Is there a similar rule to calculate the force in this case? Or should the force be 0 since the wires are perpendicular to each other?

In general, how to calculate force between two current carrying wires?

Looking forward to some guidance.

 

[DuckAmuck]

I think the force on PQ is "down" the page. Using right hand rule.

 

[gneill]

Hi Shivansh,

Please remember to use the formatting template for posts in the homework areas.

You can use a right hand rule to establish the field direction due to the XY current at locations along PQ. Then imagine a current carrier (a positive charge) moving in PQ according to the current in that wire. Use a right hand rule to determine the force direction that the moving charge would feel.

Re-drawing the setup so that the current $I$ in XY is flowing into the page, the field lines form circular paths around it:

As you can see, a positive current carrier (moving charge) in current $i$ along PQ will feel a force as determined by the right hand rule. The force on a given charge will vary with the strength of the field (distance from the current $I$).