A charged particle with speed v₀ starts at the origin along +x in a uniform field B along −z. When it crosses the y-axis, its y-coordinate is λmv₀/(2qB). Find λ.
Physics · Magnetic effect of current
JEE Mains

Question

A charged particle with speed v₀ starts at the origin along +x in a uniform field B along −z. When it crosses the y-axis, its y-coordinate is λmv₀/(2qB). Find λ.

G1 Physics · Accepted Answer

The particle moves in a circle of radius r=mv₀/(qB). Starting from the origin along +x, the next crossing of the y-axis is diametrically opposite at y=2r=2mv₀/(qB). Thus λ/2=2 and λ=4.