Question

Write the nature of path of a charged particle moving:
(i) along the electric field,
(ii) perpendicular to the electric field,
(iii) perpendicular to the magnetic field,
(iv) along the magnetic field,
(v) along the combination of electric field and magnetic field acting mutually perpendicular to each other.

Hint:

$E$-field → straight or parabolic motion; $B$-field → circular or helical motion.

Answer 1

Case (i): Along the electric field.
Force on charge: $F = qE$, acts in the direction of motion. Particle accelerates uniformly along a straight line. Case (ii): Perpendicular to the electric field.
Force $qE$ acts perpendicular to velocity, causing constant acceleration in one direction and uniform motion in the other. Resulting path is a parabola. Case (iii): Perpendicular to the magnetic field.
Force $F = qvB$ acts perpendicular to both velocity and $B$. This causes uniform circular motion with radius $r = \tfrac{mv}{qB}$. Case (iv): Along the magnetic field.
Force $F = q(\vec{v} \times \vec{B}) = 0$, since $\vec{v}$ is parallel to $\vec{B}$. Hence the particle moves in a straight line with constant velocity. Case (v): In crossed electric and magnetic fields ($E \perp B$).
- Electric field provides linear acceleration. - Magnetic field provides circular motion. - Resultant path is a helix (spiral).
Step 6: Conclusion.
The nature of path depends on field configuration: linear, parabolic, circular, or helical.