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Asked in CBSE PMT 1996 · Biot-Savart law and current element
Idea: the Biot-Savart law is an inverse-square law, so count the powers of r carefully when the numerator carries the vector ⃗r rather than the unit vector.
In terms of the unit vector: d⃗B=(μ₀)/(4π)·(i d⃗l×̂r)/(r²).
Writing ̂r=(⃗r)/r puts one more power of r into the denominator.
d⃗B=(μ₀)/(4π)·(i d⃗l×⃗r)/(r³).
The law is linear in the current, so i appears to the first power only.
That is option B.
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