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The magnetic field at a distance $r$ from a LONG STRAIGHT wire carrying current $I$ is
A$\dfrac{\mu_0\,I}{2\pi r}$
B$\dfrac{\mu_0\,I}{4\pi r}$
C$\dfrac{\mu_0\,I}{2 r^2}$
D$\dfrac{\mu_0\,I r}{2\pi}$
Answer & Solution
Correct answer: A. $\dfrac{\mu_0\,I}{2\pi r}$
1. Apply Ampere's law with a circular Amperian loop of radius $r$ centred on the wire.
2. By symmetry, $\vec{B}$ is tangential to the loop with the same magnitude everywhere on it.
3. $\oint\vec{B}\cdot d\vec{l} = B\,(2\pi r) = \mu_0 I$.
4. Solve: $B = \dfrac{\mu_0\,I}{2\pi r}$.
5. Field circles around the wire (right-hand rule: thumb along $I$, fingers curl in the direction of $\vec{B}$).
6. Option B drops a factor of 2. Option C has wrong distance dependence. Option D would grow with $r$.
_Source: NCERT Class 12 Physics Part 1, Ch 4, §4.5 (Ampere's Law applied to a long straight wire), p. 15–16._
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