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The magnetic field d⃗B due to a small current element d⃗l at a distance r, the element carrying current i, is

Asked in CBSE PMT 1996 · Biot-Savart law and current element

Answer: (2) d⃗B=(μ₀)/(4π)i(d⃗l×⃗r)/(r³)

Step-by-step solution

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.

Why the other options are wrong

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