Physics

Physics

Problem

48. A charged particle can move with constant velocity through a region containing both an electric field and a magnetic field only if the (A) electric field is parallel to the magnetic field (B) electric field is perpendicular to the magnetic field (C) electric field is parallel to the velocity vector (D) magnetic field is perpendicular to the velocity vector (A) electric field is parallel to the magnetic field (B) electric field is perpendicular to the magnetic field (C) electric field is parallel to the velocity vector (D) magnetic field is perpendicular to the velocity vector
Intuitive explanation

For a charged particle to move at constant velocity, the net force must be zero—meaning the electric and magnetic forces must cancel exactly. The magnetic force F⃗B=qv⃗×B⃗\vec{F}_B = q\vec{v} \times \vec{B} is always perpendicular to the velocity, so it can never balance an electric force along the direction of motion. The only way to achieve equilibrium is if the electric force points opposite to the magnetic force; this happens when E⃗\vec{E} is perpendicular to B⃗\vec{B}, allowing them to point in opposite directions and cancel.

Intuitive explanation

For a charged particle to move at constant velocity, the net force must be zero—meaning the electric and magnetic forces must cancel exactly. The magnetic force F⃗B=qv⃗×B⃗\vec{F}_B = q\vec{v} \times \vec{B} is always perpendicular to the velocity, so it can never balance an electric force along the direction of motion. The only way to achieve equilibrium is if the electric force points opposite to the magnetic force; this happens when E⃗\vec{E} is perpendicular to B⃗\vec{B}, allowing them to point in opposite directions and cancel.

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