A proton (charge e), traveling perpendicular to a magneticfoeld, experiences the same force as an alpha particle (charge 2e)which is also traveling perpendicular to the same field. The ratioof their speeds vproton/valpha is

a.0.5
b. 1
c. 2
d. 4
e. 8

c) 2

Explanation:

When a charged particle is moving in a region with a magnetic field, it experiences a force perpendicular to the direction of motion, therefore it starts moving with a circular motion.

The force experienced by the particle which is moving perpendicular to the field is given by

where

v is the speed of the particle

q is the charge of the particle

B is the strength of the magnetic field

Here we have:

- A proton, which has

(charge)

(speed of the proton)

B is the magnetic field

So the force experienced by the proton is

(1)

- An alpha particle, which has

(charge)

(speed of the alpha particle)

B is the magnetic field

So the force experienced by the alpha particle is

Here we are told that the force experienced by the two particles is the same, so:

And so we get:

Solving for the ratio between their speed, we find:

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measuring things 1 litre of water