Answer: option D
Explanation: when an electron is placed in a uniform magnetic field, it experiences a force, this force is responsible for the circular motion of the electron.
Hence magnetic force = centripetal force.
qvB = mv²/r
Where q = magnitude of an electronic charge
v = velocity of electron.
m = mass of electron
B = strength of magnetic field.
r = radius of circular path.
Kinetic energy = mv²/2, but we don't have this in the equation above so we manipulate by dividing both sides of equation by 2.
qvB/2 = mv²/2r
To have the kinetic energy, we multiply both sides by "r"
qvB/2 ×r = mv²/2
On the right hand side is mv²/r which is the kinetic energy.
Hence kinetic energy = (qvB/2)×r
But the expression (qvB/2) is a constant
kinetic energy = (constant) × r
Hence kinetic energy is proportional to r