Question

Two long straight parallel wires are a distance 2 d part. They carry steady equal currents flowing out of the plane of the paper. The variation of magnetic field B along the line xx’ is given by

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B

For two parallel wires carrying currents in opposite directions, the magnetic field at any point along the line joining them will have a characteristic variation. According to Ampère's law, the magnetic field due to each wire at a distance \(r\) is given by: \[ B = \frac{\mu_0 I}{2\pi r} \] Where:
\(B\) is the magnetic field,
\(\mu_0\) is the permeability of free space,
\(I\) is the current in the wire,
\(r\) is the distance from the wire. Along the line \(xx'\), the magnetic field at points between the wires will oppose each other due to the opposite directions of current.
Hence, the magnetic field will vary as shown in option (B), with the field strength decreasing towards the center and increasing as we move away from it.

The correct answer is (B) : .

Answer 2

When two parallel wires carry equal currents flowing out of the plane of the paper, the magnetic fields created by them at a point between the wires will be in the same direction, and outside the wires, the fields will be in opposite directions.

The magnetic field at a point due to a current-carrying wire is given by Ampère's Law:
\(B = \frac{\mu_0 I}{2\pi r}\)
where:
- \( I \) is the current,
- \( r \) is the distance from the wire,
- \( \mu_0 \) is the permeability of free space.

At a point between the wires, the magnetic fields from both wires will add up, and at points outside the wires, the fields will subtract. The correct variation of the magnetic field along the line \( xx' \), given the symmetry of the system and the positions of the wires, is represented by option \({B} \).