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      Question

      A current element is placed at origin. At point

      P(1 mm,1 mm), the magnetic field due to this element is:
      A Perpendicular to element and radius vector Correct Answer Incorrect Answer
      B Along current Correct Answer Incorrect Answer
      C Radial Correct Answer Incorrect Answer
      D Zero Correct Answer Incorrect Answer

      Solution

      According to the Biot-Savart law, the magnetic field due to a current element Idl at a position r is given by: B = (μ₀/4π) × (Idl × r̂)/r² Where:

      • Idl is the current element vector (assumed to be along some direction from the origin)
      • r is the position vector from the current element to point P
      • rÌ‚ is the unit vector along r
      • × represents the cross product
      Key properties of the magnetic field: 1.     The magnetic field is always perpendicular to both the current element and the radius vector (due to the cross product) 2.     The field follows the right-hand rule with respect to the current direction Looking at point P(1 mm, 1 mm):
      • The position vector r points from the origin to P
      • The cross product Idl × rÌ‚ produces a vector perpendicular to both the current element and the radius vector
      Therefore, the magnetic field at point P must be perpendicular to both the current element and the radius vector connecting the origin to point P.

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