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QPages 277-278: Q4: HC Verma: Concepts of Physics - Volume 2 Permanent Magnets Pages 277-278: Q4 Solution: Figure shows some of the equipotential surfaces of the magnetic …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often take the straight‑line separation between equipotential lines as Δx, forgetting that the magnetic field magnitude is $|\nabla V|=|\Delta V|/\Delta s$ where $\Delta s$ must be measured perpendicular to the equipotentials. Always project the spacing onto the normal direction (use $\Delta s = d\sin\theta$ if the line is drawn at angle $\theta$) before dividing the potential difference.

Figure shows some of the equipotential surfaces of the magnetic scalar potential. Find the magnetic field B at a point in the region.

Step-by-Step Verified Solution

**Answer:**

B = 2 \times 10^{-4} \text{ T}

. **Step-by-Step Explanation:** From the figure,

dx = 10 \sin 30� \text{ cm} = 0.05 \text{ m}

,

dV = 0.1 \times 10^{-4} \text{ T-m}

.

B = \left| \frac{dV}{dx} \right| = \frac{0.1 \times 10^{-4}}{0.05} = 2 \times 10^{-4} \text{ T}

[citation:17].

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