Verified Solution • 2025–26 Session moderate

QPages 228-229: Q1: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Pages 228-229: Q1 Solution: Suppose a charged particle moves with a velocity near a wire…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often equate a zero magnetic force (since $\vec v=0$) with a vanished magnetic field, overlooking that electric and magnetic fields mix under Lorentz transformation; in the particle’s rest frame a magnetic field can persist and generate an electric field that supplies the net force.

Suppose a charged particle moves with a velocity vv near a wire carrying an electric current. So, a magnetic force acts on it. If the same particle is seen from a frame moving with velocity vv in the same direction, the charge will be found to be at rest. Will the magnetic force become zero in this frame? Will the magnetic field become zero in this frame?

Step-by-Step Verified Solution

**Answer:** Yes, the magnetic force becomes zero in the moving frame. No, the magnetic field does not become zero in that frame. **Step-by-Step Explanation:** In the frame moving with the same velocity as the particle, the particle is at rest. The magnetic force is given by F⃗=qv⃗×B⃗\vec{F} = q\vec{v} \times \vec{B}. Since v⃗=0\vec{v} = 0 in this frame, the magnetic force is zero. However, the magnetic field itself is not zero. The electric and magnetic fields transform between frames according to Lorentz transformations. In the particle's rest frame, the magnetic field may be transformed into an electric field, but the magnetic field component does not simply vanish. The net electromagnetic force is still present as an electric force in the new frame.

All Questions in this Chapter

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