Motion in Combined Electric and Magnetic Fields The motion of a charged particle in a combined electric and magnetic field can be described by the vector equ...
The motion of a charged particle in a combined electric and magnetic field can be described by the vector equation:
where:
(\overrightarrow{v}) is the overall velocity of the particle
(\overrightarrow{v}_e) is the velocity due to the electric field
(\overrightarrow{v}_m) is the velocity due to the magnetic field
The electric field (\overrightarrow{E}) describes the force per unit charge experienced by a charged particle. It is a vector field, meaning it has both magnitude and direction.
where:
(q) is the charge of the particle
(\varepsilon_0) is the permittivity of free space
The electric field creates a (\overrightarrow{E}) field, which is responsible for the force experienced by a charged particle.
The magnetic field (\overrightarrow{B}) describes the force per unit charge experienced by a moving charge in a magnetic field. It is a vector field, meaning it has both magnitude and direction.
where:
(q) is the charge of the particle
(\overrightarrow{v}) is the velocity of the particle
(\overrightarrow{v_B}) is the velocity of the magnetic field
(c) is the speed of light
The magnetic field creates a (\overrightarrow{B}) field, which is responsible for the force experienced by a charged particle moving in a magnetic field.
When a charged particle moves in both an electric and magnetic field, the two fields interact with each other to produce the overall motion. The following are some important points to consider:
The electric field forces a particle to accelerate in a direction perpendicular to the electric field.
The magnetic field forces a particle to move in a direction parallel to the magnetic field.
The magnitude of the overall acceleration of the particle is given by the vector addition of the electric and magnetic field accelerations:
Examples:
A positively charged particle moving in a magnetic field will experience a force upwards.
A negatively charged particle moving in an electric field will experience a force to the left.
A particle moving in both an electric and magnetic field will experience a net force that accelerates it in a direction perpendicular to both the electric and magnetic field directions