A current element is placed at origin. At point

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
• r̂ 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 × r̂ 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.