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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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