In the laboratory, you have arranged to have a magnetic field that points north with a strength of 0.1 t and an electric field that points downward with a strength 1.2 × 107 n/c. an electric charge with a magnitude 7×10−9 c passes through the laboratory. the force on the charge due to the electric field is given by f = q e. the force on the charge due to the magnetic field is given by f = q v b, where v is the speed of the particle. the direction of the magnetic force is given by the right-hand rule. neglect the gravitational force. what direction would the charge have to travel in order for it to pass through the room undeflected? 1. east 2. west 3. south 4. north 5. upward 6. downward

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.

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:

Here's how the rule work:

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?

In other words, the charged particle shall move towards east no matter whether the charge on the particle is positive or negative.

at right angles to each other