Question

Assertion(A): A proton and an electron, with same momenta, enter in a magnetic field in a direction at right angles to the lines of the force. The radius of the paths followed by them will be same.

Reason (R): Electron has less mass than the proton.

Select the most appropriate answer from the options given below:

Options

• Both A and R are true and R is the correct explanation of A.

• Both A and R are true but R is not the correct explanation of A.

• A is true but R is false.

• A is false and R is also false.

Answer 1

Both A and R are true but R is not the correct explanation of A.

Explanation:

we know `"mv"^2/"r"`Bqv sin θ = Bqv sin θ

Centripetal force = magnetic Lorentz force

sin θ = sin 90 θ = 1  (∠ between `vec "V"` & `vec "B" = 90^circ`)

`"mv"^2/"r"` = Bqv

`"mv"/"r"` = Bq

r = `"mv"/"Bq" = "p"/"Bq" = "linear momentum"/"Bq"`

Since r = `"p"/"Bq"`

Given p, B are same

Also q for proton & electron is same except its sign.