Question

A proton moves into the page through a magnetic field of 2 T oriented to the right in the plane of the page and through an electric field of 500 V/m oriented vertically in the plane of the page. For what velocity will the proton travel straight without veering as it moves through both fields?

Answer 1

Velocity of the proton,
`v_(p) = 250 m/s`

Given:

Magnetic field, B = 2 T

Electric field, E = 500 V/m

Step-by-step explanation:

For the proton to travel in a straight line without any change in direction in both the electric and magnetic field, the forces on the proton in both the electric and magnetic fields must be equal and is given by:

`F_(E) = F_(M)`

where

`F_(E) = Force on proton in electric field`

`F_(M) = Force on proton in magnetic field`

Now,

`q_(p)E = q_(p)(\vec{v_(p)}* \vec{B})`

where

`q_(p) = charge of proton`

`v_(p) = velocity of proton`

E = electric field

`q_(p)E = q_(p)v_(p)Bsin\theta = q_(p)v_(p)Bsin90^(\circ)`

(Since,
`sin90^(\circ) = 1`)

`v_(p) = (E)/(B)`

`v_(p) = (500)/(2) = 250 m/s`