Question

The diagram shows a proton (charge q, mass m) and an alpha particle (charge 2q, mass 4m) situated in the same downward-pointing uniform field. If the field is gravitational, then both particles have the same acceleration.
What happens if the field is an electric field?

• A. Both particles still have the same acceleration because electric fields are analogous to gravitational fields.
• B. The alpha particle has greater acceleration because it has greater charge.
• C. The alpha particle has greater acceleration because it has greater mass-to-charge ratio.
• D. The proton has a greater acceleration because it has less mass.
• E. The proton has greater acceleration because it has a greater charge-to-mass ratio.

Answer 1

The correct option is E The proton has greater acceleration because it has a greater charge-to-mass ratio.

Acceleration of the proton=$\frac{F}{m}=\frac{qE}{m}$

Acceleration of the alpha particle=$\frac{F}{m}=\frac{\left(2q\right)E}{4m}=\frac{qE}{2m}$

Hence proton has greater acceleration because it has a greater charge to mass ratio.