HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q22 Solution: A long wire carrying a current is bent to form a plane along an …

QPages 249-253: Q22: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q22 Solution: A long wire carrying a current is bent to form a plane along an …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the point on the bisector as being at a constant perpendicular distance from each wire segment and directly apply $B=\mu_0 i/(2\pi r)$, which gives an incorrect $1/\sin(\alpha/2)$ dependence. In reality the distance to each element of the bent wire varies along its length, so the Biot–Savart integral must be performed; this yields the correct factor $(\pi-\alpha+\sin\alpha)$ and a $1/x$ dependence.

A long wire carrying a current

i

is bent to form a plane along an angle

\alpha

. Find the magnetic field

B

at a point on the bisector of this angle situated at a distance

x

from the vertex.

Step-by-Step Verified Solution

**Answer:**

B = \frac{\mu_0 i}{4\pi x}\left(\pi - \alpha + \sin\alpha\right)

. **Step-by-Step Explanation:** A wire bent at angle

\alpha

. The field at a point on the bisector at distance

x

is calculated by integrating the contributions from the two straight segments.

QPages 249-253: Q22: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q22 Solution: A long wire carrying a current is bent to form a plane along an …

Step-by-Step Verified Solution

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