Question

Two parallel wires carry currents of $20\text{A}$ and $40\text{A}$ in opposite directions. Another wire carrying a current antiparallel to $20\text{A}$ is placed midway between the two wires. The magnetic force on it will be

• A. Towards $20\text{A}$
• B. Towards $40\text{A}$
• C. Zero
• D. Perpendicular to the plane of the current

Answer 1

The correct option is B Towards $40\text{A}$

If A is the wire carrying current $20A$, B is the wire carrying current 40 $A$ in oppsite direction and C is the wire in the middle carrying current antiparallel to $20\text{A}$, then magnetic field produced by both the couple of wires (AC and BC) will be in same direction going inside the plane as shown in the diagram by right hand rule.
Now we know that
$\overrightarrow{F}=I(\overrightarrow{L}\times \overrightarrow{B})$
By cross product we get, due to A, the force will be towards right and due to wire B, the force on the wire will be towards right. So, both the forces will add to give a resultant force, which will be towards right, that is, towards the 40 $A$ current-carrying wire.

Also we know that parallal wires carrying current in opposite direction repel each other and parallal wires carrying current in same direction attract each other. By that rule as well we get net force to be in the direction of wire B carrying current 40 $A$.