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.