Gold ions (Au+) are accelerate to high speeds using electric fields.
These ions are then passed through a region where uniform electric E and magnetic B fields are present.
If the ions are traveling to the right, which configuration of E and B will serve as a velocity selector?
A. Electric field E up; Magnetic field B into the page
B. Electric field E down; Magnetic field B out of the page
C. Electric field E up; Magnetic field B out of the page
D. Electric field E down; Magnetic field B into the page
E. Both A and B
F. Both C and D
G. All of the above
Ridiculous.
OMG LOL!
To determine which configuration of electric and magnetic fields will serve as a velocity selector for the gold ions traveling to the right, we need to understand the principles of charge motion in electric and magnetic fields.
When a charged particle travels through an electric field, it experiences a force in the direction of the electric field lines. The magnitude of this force is given by F = qE, where q is the charge of the particle and E is the electric field strength. The direction of the force is determined by the sign of the charge.
When a charged particle travels through a magnetic field, it experiences a force perpendicular to both the magnetic field lines and its velocity. The magnitude of this force is given by F = qvB, where v is the velocity of the particle and B is the magnetic field strength. The direction of the force is determined by the cross product of the velocity and magnetic field vectors according to the right-hand rule.
To act as a velocity selector, the forces experienced by the gold ions in the electric and magnetic fields must balance out in such a way that only ions with a specific velocity are allowed to pass through. This can be achieved by setting the electric and magnetic fields in a specific configuration.
Let's analyze the given options:
A. Electric field E up; Magnetic field B into the page:
In this configuration, the electric field is in the opposite direction to the gold ions' motion, while the magnetic field is perpendicular to both the ions' motion and the electric field. Since the force experienced by the ions due to the magnetic field is perpendicular to their motion, it does not affect their velocity. Therefore, this configuration cannot serve as a velocity selector.
B. Electric field E down; Magnetic field B out of the page:
In this configuration, the electric field is in the same direction as the gold ions' motion, while the magnetic field is again perpendicular to both the ions' motion and the electric field. The force experienced by the ions due to the magnetic field is again perpendicular to their motion and does not affect their velocity. Similar to option A, this configuration cannot serve as a velocity selector.
C. Electric field E up; Magnetic field B out of the page:
In this configuration, the electric field is against the direction of the gold ions' motion, while the magnetic field is perpendicular to both the ions' motion and the electric field. The force experienced by the ions due to the electric field opposes their motion, and the force experienced due to the magnetic field is perpendicular to their motion. By appropriately adjusting the strengths of the fields, it is possible to balance these forces and allow only ions with a specific velocity to pass through. Therefore, this configuration can serve as a velocity selector.
D. Electric field E down; Magnetic field B into the page:
In this configuration, the electric field is in the same direction as the gold ions' motion, while the magnetic field is again perpendicular to both the ions' motion and the electric field. Similar to option B, the force experienced by the ions due to the magnetic field is again perpendicular to their motion and does not affect their velocity. Therefore, this configuration cannot serve as a velocity selector.
E. Both A and B:
Since option A can't serve as a velocity selector and option B is the same configuration, this choice cannot be the correct answer.
F. Both C and D:
Option D cannot serve as a velocity selector, which means this choice can't be the correct answer.
G. All of the above:
Since all the given options have been analyzed and only option C can serve as a velocity selector, this choice cannot be the correct answer.
Therefore, the correct answer is option C: Electric field E up; Magnetic field B out of the page.