While performing the mass of the electron experiment, a beam of electrons produc

Question

While performing the mass of the electron experiment, a beam of electrons produced in a tube containing helium gas under low pressure enters a region of a nearly uniform magnetic field produced by a pair of Helmholtz coils. The beam of electrons is observed to move in a circular path, and the mass of the electron can be calculated from the radius of the path. If the current through the Helmholtz coils were increased, will the radius of the circular path increase or decrease? If the accelerating voltage were increased, will the radius increase or decrease? If the magnetic field is 8.6 times 10^-4 T and the accelerating potential is 150 V, calculate the expected radius of electrons beam.

Explanation / Answer

Solution a)

For an electron of mass m moving at speed v in a circle of radius R, the magnitude of the centripetal force FC is:

FC=m*v^2/R

Therefore,

ev*B=m*v^2/R

or

e*B=m*v/R

In this case,

If I increased, therefore R decrease

Solution b)

The initial potential energy of the electrons in this experiment is eV, where V is the accelerating voltage used in the electron-beam tube. After the electrons are accelerated through a voltage V, this initial potential energy is converted into kinetic energy (1/2)mv^2. Since energy is conserved, it follows that

e*V=(1/2)m*v^2.

Combining

e/m=2*V/B^2*R^2

Then,

If accelerating voltage increased, R Increase

Solution 2)

Applying the equation:

e/m=2*V/B^2*R^2

R = 48.03 mm

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.