A proton beam is directed vertically upwards into the region between two vertical parallel metal plates, L L\,L and RRR, as shown in the diagram. Plate L L\,L is the left plate and plate R R\,R is the right plate. Plate L L\,L is maintained at a positive potential relative to plate RRR, creating a uniform horizontal electric field pointing from left to right.
To keep the path of the protons vertical and undeflected, a uniform magnetic field is applied in the region between the plates.
Determine the direction of the magnetic field required to allow the proton beam to pass undeflected. Explain your reasoning by reference to the forces acting on the protons.
The speed of the protons entering the region is now decreased. Explain how the path of the protons can be restored to a straight vertical line by adjusting:
- only the electric field strength EEE
- only the magnetic flux density B B\,B
Include the relevant algebraic relationship for key variables.
A physics student proposes that if a beam of alpha particles (He2+\text{He}^{2+}He2+) was used instead of protons at the same initial speed, they would also pass through the crossed fields undeflected without changing E E\,E or BBB. Discuss whether this statement is correct by reference to the specific charge of both particles.