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Physics Question on Magnetic Force

Two identical charged particles enter a uniform magnetic field with same speed but at angles 30∘^\circ and 60∘^\circ with field. Let a , b and c be the ratio of their time periods, radii and pitches of the helical paths then:

A

abc = 1

B

abc > 1

C

abc < 1

D

ac = b

Answer

abc = 1

Explanation

Solution

T=2πmqB,R=mvabpitch=T×cos⁡45∘T=\frac{2 \pi m}{qB},R =\frac{mv}{ab} pitch =T \times \cos 45^{\circ}