A charged particle enters a uniform magnetic field with a velocity vector at an angle of 45 ° with the magnetic field. The pitch of the helical path followed by the particle is p . The radius of the helix will be -

Step-by-step solution

Pitch of helical path is, p = v cos ⁡ θ × 2 π m q B = 2 π m v cos ⁡ 45 ° q B = 2 π m v 2 q B Also radius of helix is, r = m v sin ⁡ θ q B = m v 2 q B ∴ r p = m v 2 q B × 2 q B 2 π m v = 1 2 π or r = p 2 π