Verified Solution • 2025–26 Session moderate

QPages 248-249: Q12: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 248-249: Q12 Solution: Consider a long, straight wire of cross-sectional area A…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently assume the magnetic field of a steady current is the same for every observer, overlooking that current is defined relative to the observer's frame. When the observer moves with the electron drift speed $v=i/(nAe)$, the electrons are stationary and the positive lattice moves opposite, canceling the net charge flow; thus the magnetic field vanishes (while an electric field emerges).

Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free electrons per unit volume. An observer places himself on a trolley moving in the direction opposite to the current with a speed v=i/nAe)v = i/ nAe) and separation from the wire by a distance rr. The magnetic field seen by the observer is very nearly

Multiple Choice Options

  • A μ0i2πr\frac{\mu_0 i}{2\pi r}
  • B zero
  • C μ0iπr\frac{\mu_0 i}{\pi r}
  • D 2μ0iπr\frac{2\mu_0 i}{\pi r}

Step-by-Step Verified Solution

**Answer:** (b) zero. **Step-by-Step Explanation:** The observer moves with the drift velocity of the electrons. In the observer's frame, the electrons are at rest. The positive ions move with velocity -v. The net current in the observer's frame is zero, so the magnetic field is zero.

All Questions in this Chapter

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