Verified Solution • 2025–26 Session moderate

QPage 249: Q1: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Page 249: Q1 Solution: The magnetic field at the origin due to a current element…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often confuse the direction of the cross product, incorrectly assuming $d\vec{l} \times \vec{r}$ instead of $\vec{r} \times d\vec{l}$, which flips the sign of the magnetic field vector. Remember that the standard Biot-Savart law is defined as $d\vec{B} = \frac{\mu_0 i}{4\pi} \frac{\vec{r} \times d\vec{l}}{r^3}$, where $\vec{r}$ points from the source element to the observation point.

The magnetic field at the origin due to a current element idl⃗i d\vec{l} placed at a position r⃗\vec{r} is

Multiple Choice Options

  • A μ0i4πdl⃗×r⃗r3\frac{\mu_0 i}{4\pi} \frac{d\vec{l} \times \vec{r}}{r^3}
  • B −μ0i4πr⃗×dl⃗r3-\frac{\mu_0 i}{4\pi} \frac{\vec{r} \times d\vec{l}}{r^3}
  • C μ0i4πr⃗×dl⃗r3\frac{\mu_0 i}{4\pi} \frac{\vec{r} \times d\vec{l}}{r^3}
  • D −μ0i4πdl⃗×r⃗r3-\frac{\mu_0 i}{4\pi} \frac{d\vec{l} \times \vec{r}}{r^3}

Step-by-Step Verified Solution

**Answer:** (c) (__i/4�)(r _ dl)/r_. **Step-by-Step Explanation:** The Biot-Savart law gives dB = (__i/4�)(dl _ __)/r_. This is equivalent to (c) with the correct sign convention.

All Questions in this Chapter

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