Question

An ion-source is at distance d from a flat, horizontal collector at the same potential as the source. A magnetic field of flux density B acts horizontally (Magnetic ild line go from the Left side towards the Right side). The field is uniform throughout the region between the source and the collector.

An ion of charge q and mass m is emitted vertically downwards at speed v. Under what conditions the ion reach the collector?

A. v > √2Bq/m
B. v < √2Bq/m
C. v > dBq/m
D. v < dBq/m

Kindly, tell me how to solve this question, please.

Thank you.

Answer 1

$$F=ma=m\frac{v^2}{d}\\F=qBv\sin{\theta}\\m\frac{v^2}{d}=qBv\sin{\theta}$$

$$v=\frac{qBd\sin{\theta}}{m}<\frac{qBd}{m}$$

It is because $\sin{\theta}$ cannot be greater than 1.

Answer: D. v < dBq/m