Question

A charged particle moves through a magnetic field in a direction perpendicular to it. Then the

• A. acceleration remains unchanged
• B. velocity remains unchanged
• C. speed of the particle remains unchanged
• D. direction of the particle remains unchanged

Answer 1

Answer: (C)

speed of the particle remains unchanged

Answer 2

When a charged particle moves through a magnetic field in perpendicular direction, then the charged particle follow a circular path and a magnetic force (F) acts on it which changes the direction of particle but does not alter the magnitude of itsvelocity(i.e. speed). The force acting on the particle is given by,

$F = qv \times B$

Thus, the speed of the particle remains unchanged.

Note: If a charged particle moves at $45^{\circ}$ to magnetic field then path of the particle will be a helix whose circular part has radius as per the relation
$r=\frac{m v \sin \theta}{q B}$