Respuesta :
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
Answer:
B) K.E is proportional to r²
Explanation:
The motion of particle in magnetic field is caused by lorentz force.
F=qvB--(1)
v= Velocity of particle
q=magnitude of charge
B=Strength of magnetic field
To move the object in circular path, centripetal force is
[tex]F_c=\frac{mv^2}{r}--(2)[/tex]
Which must be equal to lorentz force. So equating (1) and(2)
[tex]\frac{mv^2}{r}=qvB\\\\v=\frac{qrB}{m}--(3)[/tex]
K.E is given as:
[tex]K.E=\frac{1}{2}mv^2[/tex]
Substituting values of v from (3) in above:
[tex]K.E=\frac{1}{2}m(\frac{qrB}{m})^2\\\\K.E=\frac{(qrB)^2}{2m}[/tex]
Which shows K.E is directly proportional to r^2
