a particle with a positive charge of 3c moves downward at speed of 15m/s. It passes simultaneously through a magnetic field of 0.2T directed into th page and an electric field of 3N/C directed to the right. how is the motion of the particle affected?
To determine how the motion of the particle is affected, we need to consider the forces acting on it.
1. Magnetic force: The magnetic force on a charged particle moving through a magnetic field is given by the equation F = q * v * B * sin(θ), where F is the force, q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field direction. In this case, the particle has a positive charge of 3c and is moving downward (opposite to the magnetic field direction). Therefore, θ = 180 degrees, and the force due to the magnetic field is Fmagnetic = (3c)(15 m/s)(0.2 T) * sin(180 degrees).
2. Electric force: The electric force on a charged particle in an electric field is given by the equation F = q * E, where F is the force, q is the charge, and E is the electric field strength. The particle has a positive charge of 3c and the electric field is directed to the right. Therefore, Felectric = (3c)(3 N/C).
Now, to determine the overall effect on the motion of the particle, we need to compare the magnitudes and directions of these forces.
If the magnetic force is greater than the electric force, the motion of the particle will be influenced primarily by the magnetic field.
If the electric force is greater than the magnetic force, the motion of the particle will be influenced primarily by the electric field.
If the two forces are equal in magnitude, the motion of the particle will be affected by both forces simultaneously.
To determine which force is greater, we need to calculate the magnitudes of the forces and compare them:
Fmagnetic = (3c)(15 m/s)(0.2 T) * sin(180 degrees)
Felectric = (3c)(3 N/C)
Here, we should note that the magnitude of the charge, |q|, is important because it determines the magnitude of the forces. Assuming |c| = 1, |q| = 3.
Plugging in the values, we get:
Fmagnetic = (3)(15)(0.2) * sin(180 degrees) = -18 N
Felectric = (3)(3) = 9 N
Since the magnitude of the electric force (9 N) is greater than the magnitude of the magnetic force (18 N), the particle's motion will be primarily influenced by the electric field. Specifically, it will be accelerated to the right due to the electric field. The magnetic field will have a negligible effect on the motion of the particle.