Electrons (mass m, charge -e)are accelerated from rest through a potential difference V and are then deflected by a magnetic field that is perpendicular to their velocity.The radius of the resulting electron trajectory is:
E)none of these

Question

Electrons (mass m, charge -e)are accelerated from rest through a potential difference V and are then deflected by a magnetic field  that is perpendicular to their velocity.The radius of the resulting electron trajectory is:
E)none of these

Quizplus · Accepted Answer

The radius of an electron trajectory in a magnetic field is given by the formula:

r = mv/eB

where 
m = mass of electron 
v = velocity of electron 
e = charge on electron 
B = magnetic field

The velocity of the electron after being accelerated through a potential difference V is given by the formula:

v = sqrt(2eV/m)

Substituting this value of v in the above formula for r, we get:

r = m(sqrt(2eV/m))/eB

Simplifying:

r = sqrt(2mV)/Be

Since the magnetic field is perpendicular to the velocity, we can use the right-hand rule to determine that the force on the electron is directed towards the center of the circle, and is given by:

F = evB

Setting this equal to the centripetal force:

F = mv^2/r

We get:

evB = mv^2/r

Substituting v from earlier:

eB(sqrt(2eV/m)) = m(2eV/m)/r

Simplifying:

r = sqrt(2mV)/(eB)

Thus the correct option is C.

Electrons (Mass M, Charge -E)are Accelerated from Rest Through a Potential