Questions: A proton (charge e ), traveling perpendicular to a magnetic field, experiences the same force as an alpha particle (charge 2e ) which is also traveling perpendicular to the same field. The ratio of their speeds, vproton / valpha is 0.5 4 1 8 2

Solution Steps

We need to find the ratio of the speeds of a proton and an alpha particle when both are traveling perpendicular to the same magnetic field and experiencing the same magnetic force.

The magnetic force \( F \) on a charged particle moving perpendicular to a magnetic field \( B \) is given by: \[ F = q v B \] where \( q \) is the charge of the particle and \( v \) is its speed.

Given that the proton and the alpha particle experience the same force: \[ F_{\text{proton}} = F_{\text{alpha}} \] Substituting the formula for magnetic force: \[ e v_{\text{proton}} B = 2e v_{\text{alpha}} B \]

Cancel out the common terms \( e \) and \( B \): \[ v_{\text{proton}} = 2 v_{\text{alpha}} \]

The ratio of their speeds is: \[ \frac{v_{\text{proton}}}{v_{\text{alpha}}} = 2 \]

Final Answer