Verified Solution • 2025–26 Session moderate

QPages 228-229: Q6: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 228-229: Q6 Solution: An electron beam projected along the positive -axis deflects…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often apply the right‑hand rule to $\vec v\times\vec B$ without accounting for the electron’s negative charge, thus reversing the inferred field direction; remember the magnetic force on an electron is $\vec F = -e\,\vec v\times\vec B$, so the force is opposite to the $\vec v\times\vec B$ direction. Also, only the component of $\vec B$ perpendicular to $\vec v$ matters, so the field need not be strictly along $\pm z$—it may have any parallel (x‑axis) component without affecting the deflection.

An electron beam projected along the positive xx-axis deflects along the positive yy-axis. If this deflection is caused by a magnetic field, what is the direction of the field? Can we conclude that the field is parallel to the zz-axis?

Step-by-Step Verified Solution

**Answer:** The magnetic field is along the positive z-axis. Yes, we can conclude it is parallel to the z-axis (or at least has a component along it). **Step-by-Step Explanation:** The electron moves along the positive x-axis and is deflected along the positive y-axis. The force F⃗=−e(v⃗×B⃗)\vec{F} = -e(\vec{v} \times \vec{B}) must point in the +y direction. Using the right-hand rule (with the negative charge reversing the direction), v⃗×B⃗\vec{v} \times \vec{B} must point in the -y direction. If v⃗\vec{v} is along +x, then B⃗\vec{B} must be along +z to give i^×k^=−j^\hat{i} \times \hat{k} = -\hat{j}.

All Questions in this Chapter

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