A portion is fired from origin with velocity `vec(v) = v_(0) hat(j)+ v_(0) hat(k)` in a uniform magnetic field `vec(B) = B_(0) hat(j)`. In the subsequent motion of the proton

Options

A. its z co-ordinate can never be negative
B. its x co-ordinate can never be positive
C. its x and z co-oridinate cannot be zero at the same time
D. its y co-ordinate will be proportional to its time of flight

Answer

B, D

Explanation

Velocity of proton makes an angle of `45^(@)` with the direction of magnetic field.

Therefore, path of the proton is a helix. The plane of the circle of this helix is the plane formed by negative x and -axis. Therefore, x-coordinate can never be positive and z co-ordinate will become zero simultaneously after every pitch and y co-ordinate of proton at any time t is `y=v_(0)t` i.e. `y prop t`.