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 charged particle is affected by the magnetic and electric fields, we need to analyze the forces acting on the particle.
1. Magnetic Force: The magnetic force acting on a charged particle moving in a magnetic field is given by the equation Fm = qvBsinθ, where Fm is the magnetic force, q is the charge, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.
In this case, the particle has a charge of 3c (coulombs), and it is moving downward at a speed of 15 m/s. The magnetic field is directed into the page, which is perpendicular to the velocity vector of the particle. Therefore, the angle between the velocity and magnetic field vectors is 90 degrees (θ = 90 degrees).
Using the formula for the magnetic force and plugging in the values:
Fm = (3c)(15 m/s)(0.2 T)(sin 90°)
Fm = 9c(0.2)
Fm = 1.8c N
The magnetic force experienced by the particle is equal to 1.8c Newtons, directed to the left.
2. Electric Force: The electric force acting on a charged particle in an electric field is given by the equation Fe = qE, where Fe is the electric force, q is the charge, and E is the electric field strength.
In this case, the particle has a positive charge of 3c, and it is subjected to an electric field of 3 N/C directed to the right.
Using the formula for the electric force and plugging in the values:
Fe = (3c)(3 N/C)
Fe = 9c N
The electric force experienced by the particle is equal to 9c Newtons, directed to the right.
Now, let's analyze the motion of the particle based on the forces acting on it:
The particle experiences a magnetic force of 1.8c Newtons directed to the left and an electric force of 9c Newtons directed to the right. These forces act in opposite directions, and their magnitudes are different.
The resulting motion of the particle will be influenced by the combined effect of these forces. The particle will experience a net force of (9c - 1.8c) Newtons = 7.2c Newtons directed to the right.
Therefore, the particle will be accelerated to the right due to the net electric force acting on it. The magnetic force does not affect the particle's overall motion significantly in this case, as its magnitude is much smaller than the electric force.
In summary, the motion of the particle is primarily influenced by the electric field, causing it to accelerate to the right.