Verified Solution • 2025–26 Session moderate

QPages 249-253: Q48: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q48 Solution: A long, cylindrical tube of inner and outer radii and carries a …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that the current flowing in the tube’s wall contributes to the Ampèrian loop inside the hollow region, leading them to calculate a non‑zero $B$ for $r<a$. Remember that an Amperian circle drawn entirely inside the cavity encloses no current, so $B=0$ there. Likewise, for the field just outside the tube the loop radius must be $r=b$, the outer surface, not the inner radius $a$, giving $B=\mu_0 i/(2\pi b)$.

A long, cylindrical tube of inner and outer radii

a

and

b

carries a current

i

distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point a) just inside the tube b) just outside the tube.

Step-by-Step Verified Solution

**Answer:** (a) Just inside: 0 (b) Just outside:

\frac{\mu_0 i}{2\pi b}

. **Step-by-Step Explanation:** (a) Inside the hollow part of the tube,

B = 0

. (b) Just outside the tube at radius

b

:

B = \frac{\mu_0 i}{2\pi b}

.

All Questions in this Chapter

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