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Question:

A long wire with a small current element of length 1cm is placed at the origin and carries a current of 10A along the X-axis. Find out the magnitude and direction of the magnetic field due to the element on the Y-axis at a distance 0.5m from it.

Solution:

Q1=Q2=45° (0.5/0.5 = tan θ)
Q1=45°
B = μ0/4π * (l*r) * (sin φ1 + sin φ2) = μ0/4π × 10(0.5 × 10⁻² ) × (sin 45° + sin 45°) = 10⁻⁷ × 10/0.5 × 10⁻² × 2
B = 2.8 × 10⁻⁸ π