Compass Behavior Near Parallel Current-Carrying Wires

[Samurai44]

Homework Statement

two wires are parallel to each other,carries current of same magnitude, and the distance between them is 10cm ,, wire A carries current out of the page ,, Wire B carries current into the page ... A compass is placed at 4 cm from wire A .. Where does the needle point ?

I also would like to know where does the needle will point if the two wires carries same current direction

Homework Equations

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same current direction - Attraction
opposite current direction - Repulsion

The Attempt at a Solution

I drew the magnetic field around each wire(Wire A-Anticlockwise ... Wire B-Clock wise) , but since the field is circular around a straight wire , so I couldn't know where it will point exactly .

 

[gneill]

I drew the magnetic field around each wire(Wire A-Anticlockwise ... Wire B-Clock wise) , but since the field is circular around a straight wire , so I couldn't know where it will point exactly .

It will be tangent to the circle at any location around the circle.

 

[Samurai44]

It will be tangent to the circle at any location around the circle.

so the other wire won't affect the direction of the needle unless the compass was at mid point ?

 

[gneill]

so the other wire won't affect the direction of the needle unless the compass was at mid point ?

No, the fields from both wires will sum at any given location (superposition principle). Pick a location and sketch the circles centered on each wire that pass though that point. Sketch in the field vector at that point for each wire. Sum the vectors.

 

[Samurai44]

No, the fields from both wires will sum at any given location (superposition principle). Pick a location and sketch the circles centered on each wire that pass though that point. Sketch in the field vector at that point for each wire. Sum the vectors.

alright thanks