A particle of mass m and charge q is incident on XZ plane with velocity v in a direction making angle θ with a uniform magnetic field applied along X-axis. The nature of motion performed by the particle is

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(2) Helical. Given: speed v at an angle θ to a uniform field ⃗B along the X axis. Idea: split the velocity into a part along ⃗B and a part across it, and treat the two separately. Along the field: v cos θ gives ⃗v×⃗B=0, no force, so this part stays constant and drifts the particle steadily along X. Across the field: v sin θ feels qvB sin θ and bends into a circle of radius (mv sin θ)/(qB) in the plane perpendicular to X. A steady drift along the axis added to a circle about that axis traces a helix.

A particle of mass m and charge q is incident on XZ plane with velocity v in a direction making angle θ with a uniform magnetic field applied along X-axis. The nature of motion performed by the particle is

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