A uniform magnetic field of B = 3x10−4 T points in the positive x direction. A charge of 6 μC is fixed at the origin and a charge of −3μC is fixed at (2,0) on the x axis. A charge of 4 μC travels on the y axis at 5.0 x 106 m/s. Neglecting gravity, what force does the moving charge experience when it is 6.0 nm above the origin? Give your answer as a vector (that is, with both magnitude and direction).

To find the force experienced by the moving charge, we need to consider the magnetic force on a charged particle moving through a magnetic field. The magnetic force is given by the equation:

F = q v B sin(theta),

where:
- F is the force,
- q is the charge,
- v is the velocity of the moving charge,
- B is the magnetic field,
- theta is the angle between the velocity vector and the magnetic field vector.

To determine the direction of the force, we can use the right-hand rule:

- Point the thumb of your right hand in the direction of the velocity vector.
- Curl your fingers toward the direction of the magnetic field vector.
- Your extended palm will indicate the direction of the force.

Now let's apply this formula to our problem:

- q = 4 μC = 4 x 10^-6 C (convert microCoulombs to Coulombs).
- v = 5.0 x 10^6 m/s (given).
- B = 3 x 10^-4 T (given).

First, let's calculate the angle theta:

- The moving charge is traveling along the y-axis, perpendicular to the x-axis magnetic field. Therefore, theta = 90 degrees.

Now, we can calculate the force experienced by the moving charge:

F = (4 x 10^-6 C) x (5.0 x 10^6 m/s) x (3 x 10^-4 T) x sin(90 degrees).

Since sin(90 degrees) = 1, the equation simplifies to:

F = (4 x 10^-6 C) x (5.0 x 10^6 m/s) x (3 x 10^-4 T) = 6 x 10^-4 N.

So, the magnitude of the force experienced by the moving charge is 6 x 10^-4 N.

To find the direction of the force, we need to apply the right-hand rule:

- Point your thumb up the y-axis (positive direction).
- Curl your fingers toward the positive x-axis (direction of the magnetic field B).
- Your extended palm will indicate the direction of the force.

Based on this, the force experienced by the moving charge is directed in the negative z-direction (downwards).

Therefore, the force experienced by the moving charge when it is 6.0 nm above the origin is F = -6 x 10^-4 N in the negative z-direction.