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Question

A charged particle enters into a uniform magnetic field with velocity vector at an angle of 45o with the magnetic field. The pitch of the helical path followed by the particle is p. The radius of the helix will be
  1. p2π
  2. 2p
  3. p2π
  4. 2pπ

A
p2π
B
2p
C
p2π
D
2pπ
Solution
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Pitch of the helix is product of velocity component along the magnetic field and the time period T.

Pitch: p=2πmqBvcosθ=2πPcosθqB=2πPcos450qB
Here P denotes momentum
Radius of the helix: r=mvsinθqB=mvsin450qB=Psin450qB

p=2πr

r=p2π

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