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A long straight wire of circular cross-section (radius a) carries a uniformly distributed steady current I. For a point inside the wire at distance r < a, the magnetic field varies as:
AB ∝ r
BB ∝ 1/r
CB ∝ 1/r²
DB ∝ r²
Answer & Solution
Correct answer: A. B ∝ r
1. For $r < a$, the enclosed current is the fraction in area $\pi r^2$: $I_e = I\dfrac{r^2}{a^2}$.
2. Ampère's law: $B(2\pi r) = \mu_0 I_e = \mu_0 I\dfrac{r^2}{a^2}$.
3. Solve: $B = \dfrac{\mu_0 I}{2\pi a^2}\,r$.
4. With $a$ fixed, $B \propto r$ (the $1/r$ behaviour applies only outside, for $r > a$).
_Source: NCERT Class 12 Physics Ch 4 "Moving Charges and Magnetism", p.151_
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