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
You want the forces of the E and B selectors to be equal and opposite at the chosen velocity, all other velocities, B and E are not equal, and the ions will deflect one way or the other.
So choose an E, either up, or down.
Say UP. Then the positive gold ions will deflect up due to E. Now, the idea is to have B deflect them down.
There are a number of right hand rules:
http://physicsed.buffalostate.edu/SeatExpts/resource/rhr/rhr.htm
So, B must be out of the paper.
But it could be reversed, E force down, then B would be...
Pick a right hand rule, memorize it. They all work.
To determine which configuration of electric and magnetic fields will serve as a velocity selector, we need to understand the principles of charged particle motion in electric and magnetic fields.
When a charged particle moves through a magnetic field, it experiences a force perpendicular to both the velocity of the particle and the magnetic field. This force is given by the equation F = qvBsinθ, where F is the force, q is the charge of the particle, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field.
When a charged particle moves through an electric field, it experiences a force equal to F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength.
In order to act as a velocity selector, the electric and magnetic fields must be configured in such a way that they exert forces on the ions that counterbalance each other. This means that the electric force and the magnetic force must be equal and opposite, which can be achieved by adjusting the strength and orientation of the fields.
Let's consider each option:
A. Electric field E up; Magnetic field B into the page
If the ions are traveling to the right, the magnetic force will be directed downward, while the electric force will be directed upward. These forces are not equal and opposite, so this configuration is not a velocity selector.
B. Electric field E down; Magnetic field B out of the page
If the ions are traveling to the right, the magnetic force will be directed upward, while the electric force will be directed downward. These forces are not equal and opposite, so this configuration is also not a velocity selector.
C. Electric field E up; Magnetic field B out of the page
If the ions are traveling to the right, the magnetic force will be directed downward, while the electric force will be directed upward. These forces are equal and opposite, so this configuration can serve as a velocity selector.
D. Electric field E down; Magnetic field B into the page
If the ions are traveling to the right, the magnetic force will be directed upward, while the electric force will be directed downward. These forces are equal and opposite, so this configuration can also serve as a velocity selector.
E. Both A and B
As discussed earlier, neither option A nor option B alone can serve as a velocity selector.
F. Both C and D
Both option C and option D can serve as velocity selectors, as explained above.
G. All of the above
Option G is incorrect because options A and B cannot serve as velocity selectors.
Therefore, the correct answer is option F: Both C and D.