Question

It is found that a non-zero current is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is:

• A. must be 45°
• B. may be 0° or 180°
• C. must be 90°
• D. may be 30° or 60°

Answer 1

The Correct Option is B

The correct option is: (B): may be 0° or 180°.

Ampère's law states that the circulation of the magnetic field (B) around a closed path is directly proportional to the total current (I through the path enclosed by that path. Mathematically, this is expressed as:

∮B⋅dl=μ0​⋅Ienclosed​,

where μ0​ is the permeability of free space.

Now, if a non-zero current is unable to produce any magnetic field at a particular point, it implies that the current enclosed within any closed path around that point is zero (enclosed​=0). According to Ampère's law, if enclosed​=0, then the circulation of the magnetic field (∮B⋅dl) around any closed path is also zero.

The circulation of the magnetic field around a closed path is related to the angle between the current element and the position vector. The angle between the two vectors would affect the component of the current that contributes to the magnetic field at that point. If there's no magnetic field, it suggests that the angle between the current element and the position vector is such that the component of the current along the position vector is zero. This can happen when the angle is either 0° or 180°.

In other words, the current element is either parallel (0°) or antiparallel (180°) to the position vector. These orientations result in no contribution to the magnetic field at that particular point, leading to the observed absence of a magnetic field despite the presence of a non-zero current.

Hence, the answer of "0° or 180°" is justified based on the principle that the current element's orientation either parallel or antiparallel to the position vector results in no magnetic field at that specific point.