Answer:
Choice 1: The particle shall move eastward as it travels through the room.
The electrical and magnetic force on the particle shall balance no matter whether the charge on the particle is positive or negative.
Step-by-step explanation:
The question gives the magnitude of the charge on the particle but doesn't say anything about the sign of the charge on the particle. However, it turns out that whether this sign is positive or negative make no difference.
Start by considering the case that the charge on the particle is positive. What will be the direction of the electrical force on the particle?
The direction of an electrical field is same as the direction of electrical force on a particle with a positive charge. The electrical field in this room points downwards, which means that the direction of the electrical force on a positive charge will also point downward.
The particle will deflect downwards if the electrical force is the only force that acts on it. For the particle to go through the room undeflected, the net force on the particle shall be zero. The magnetic force shall balance the downward electrical force. In other words, the magnetic force on the positive particle shall point upwards.
The right-hand grip rule relates the following:
- The direction of the nominal current due to a moving charge (in the same direction of the velocity of a positive charge and opposite of that of a negative charge,)
- The direction of the magnetic field, and
- The direction of the magnetic force on the moving charge.
Here's how the rule work:
- Open the right hand such that all five fingers are in the plane of the palm.
- Start by pointing all four fingers of the right hand, excepting the thumb, in the direction of the nominal current (again, that's the same as the direction of the velocity of a positive charge and opposite of that of a negative charge.)
- Rotate the right forearm, such that when the four finger are bent inward 90° out of the palm, they point in the direction of the magnetic field
- The thumb will now point in the direction of the magnetic force on the moving charge.
In this case, the magnetic field points toward the north (to the front). Therefore, when the four fingers are turned by 90° out of the palm, they shall point to the north. The magnetic force points upwards, such that the thumb shall point upward. Now, open the right hand such that the four fingers are in the plane of the palm. The four fingers now point toward the right, which is the same as east. In other words, by the right-hand rule, the conventional current shall point to the east of the room. The particle is assumed to be positive. To generate that eastbound current, the particle shall also move eastwards.
Now, what if the charge on the particle is negative?
- The direction of the electrical force on the negative charge will be the opposite as the direction of the electrical field. That is: the electrical force on the particle points upwards.
- The magnetic force on the particle shall point downwards to balance the electrical force.
- Apply the right-hand grip rule. Again, the four finger will point towards north (to the front) in the direction of the magnetic field when turned 90° out of the palm. However, the thumb shall point downwards in the direction of the magnetic force. Now, open the palm and the four fingers will point to the left (to the west.) That's the direction of the conventional current. However, the particle is now assumed to be negative. To generate a westbound conventional current, the negative charge needs to move in the opposite direction to the east.
In other words, the charged particle shall move towards east no matter whether the charge on the particle is positive or negative.