Verified Solution • 2025–26 Session moderate

QPages 277-278: Q6: HC Verma: Concepts of Physics - Volume 2 Permanent Magnets Pages 277-278: Q6 Solution: Show that the magnetic field at a point due to a magnetic…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently confuse the angle of the magnetic field with the position angle by omitting the factor of 2 in the relation $\tan \alpha = \frac{1}{2} \tan \theta$. Always derive or recall that the field angle $\alpha$ is not equal to $\theta$, but satisfies $\tan \alpha = \frac{\tan \theta}{2}$.

Show that the magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis if the line joining the point with the centre of the dipole makes an angle of tan⁡−12)\tan^{-1}\sqrt{2}) with the magnetic axis.

Step-by-Step Verified Solution

**Answer:** θ+α=90�\theta + \alpha = 90�, so the field is perpendicular to the axis. **Step-by-Step Explanation:** Given tan⁡θ=2\tan \theta = \sqrt{2}. The angle α\alpha of the resultant field with the axis satisfies tan⁡α=tan⁡θ2=22=12\tan \alpha = \frac{\tan \theta}{2} = \frac{\sqrt{2}}{2} = \frac{1}{\sqrt{2}}. Thus tan⁡α=cot⁡θ=tan⁡(90�−θ)\tan \alpha = \cot \theta = \tan(90� - \theta), so α=90�−θ\alpha = 90� - \theta, giving θ+α=90�\theta + \alpha = 90� [citation:17].

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