Question

Any charged particle enters in a uniform magnetic field at an angle θ (where 0°< θ < 90°). How will be the path of the particle? Calculate its pitch.

Answer 1

Answer:

helical path,2Πmvcosθ/qB

Explanation:

when a paticle enters magnetic field with 0⁰ angle it travels in striaght line.

when particle enters with90° then circular path.

during circular path we can find time of revolution which is required for pitch caluclation.

helicalis a path in which particle moves in circle and moves forward at a same time so we are taking the time from circular motion so that when caluclating pitch (d)=v*T , where t is time of revolution.

since circular motion F=mv²/r ,and magnetic force F=q(V×B){where v is perpendicular to B since angle 90⁰} so F=qvB,

mv²/r=qvB;

r=mv/qB; (v=rωπ)so v/r=ω;

qB/m=ω;

Time period T=2π/ω

T=2πm/qB

now in helical case v can resolved into two components i.e. vcosθ(along magnetic field),vsinθ(perendicular to magnetic field)

now d=vcosθ*2πm/qB