Question

The pattern of magnetic field due to a current carrying wire depends upon the shape made by that wire. Justify.

Hint:

Biot-Savart law: Field depends on distance, angle, and current element direction. Different shapes \(\Rightarrow\) different distributions of elements \(\Rightarrow\) different field patterns.

Answer 1

The Pattern of Magnetic Field Due to a Current Carrying Wire Depends Upon the Shape of the Wire – Justification:

When an electric current flows through a conductor, it produces a magnetic field around it. The pattern, direction, and strength of this magnetic field depend on the shape and arrangement of the current-carrying conductor. Therefore, different shapes of wires produce different magnetic field patterns.

1. Straight Current-Carrying Conductor:

– The magnetic field lines form concentric circles around the straight wire.
– The direction of the field is given by the Right-Hand Thumb Rule.
– The field strength decreases as the distance from the wire increases.

Thus, a straight wire produces circular magnetic field lines around it.

2. Circular Loop Carrying Current:

– The magnetic field lines near the wire are circular.
– At the center of the loop, the field lines become almost straight and parallel.
– The magnetic field at the center is stronger compared to that of a straight wire.

Therefore, bending the wire into a circular loop changes the magnetic field pattern and increases its strength at the center.

3. Solenoid (Coiled Wire):

– A solenoid produces a magnetic field similar to that of a bar magnet.
– The field lines inside the solenoid are straight, parallel, and closely spaced, indicating a strong and uniform magnetic field.
– Outside the solenoid, the field lines resemble those of a bar magnet.

Thus, coiling the wire into a solenoid produces a completely different magnetic field pattern.

Conclusion:
The magnetic field pattern produced by a current-carrying wire depends on the shape of the wire. A straight wire produces circular field lines, a circular loop produces a stronger field at the center, and a solenoid produces a bar-magnet-like field. Hence, the shape of the conductor determines the magnetic field pattern.