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QPage 248: Q6: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Page 248: Q6 Solution: A long, straight wire carries a current. Is Ampere's law valid…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often mistakenly believe Ampere's law only applies to circular loops centered on the wire, confusing the law's universal validity with the specific symmetry required to calculate $B$. Remember that $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$ holds for any closed path, even if the integral is non-zero and non-trivial to evaluate without symmetry.

A long, straight wire carries a current. Is Ampere's law valid for a loop that does not enclose the wire, or that encloses the wire but is not circular?

Step-by-Step Verified Solution

**Answer:** Yes, Ampere's law is valid for any closed loop, whether or not it encloses the wire, and whether or not it is circular. **Step-by-Step Explanation:** Ampere's law ∮B⃗⋅dl⃗=μ0ienclosed\oint \vec{B} \cdot d\vec{l} = \mu_0 i_{enclosed} is universally valid for any closed loop. If the loop does not enclose the wire, ienclosed=0i_{enclosed} = 0, so the line integral is zero. The shape of the loop does not matter.

All Questions in this Chapter

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