Particle Trajectory in Combined E and BHardQuestion 20223
Question
A positive charge q enters a region where E points upward and B points out of the page. For the charge to move undeflected in the horizontal direction, which condition must hold?
- AqE = qvB (upward electric force = downward magnetic force)Correct
- BE = vB²
- Cv = B/E
- DqE = qvB with electric force downward and magnetic force upward
Correct answer
qE = qvB (upward electric force = downward magnetic force)
Explanation
The electric force on +q is upward (qE upward). For horizontal motion in +x direction and B out of page (+z): magnetic force = q(v×B) = q(vx̂×Bẑ) = qvB(x̂×ẑ) = −qvBŷ (downward). Equilibrium: qE = qvB → v = E/B. This is the velocity selector principle.