a MAGNET CAN EXERT A FORCE ON A MOVING CHARGED PARTICLE, BUT IT CAN NOT CHANGE THE PARTICLE'S KINETIC ENERGY. WHY?
The force that a magnetic field exerts on a charge is always perpendicular to the direction of motion. Work is only done by the force component along the direction of motion, and that component is always zero.
A magnet can indeed exert a force on a moving charged particle due to the interaction between the magnetic field generated by the magnet and the magnetic field associated with the particle's motion. This force is known as the Lorentz force and is given by the equation:
F = q(v x B)
Where:
F is the force experienced by the charged particle,
q is the charge of the particle,
v is the velocity of the particle,
B is the magnetic field.
However, despite the force exerted by the magnet, it cannot change the particle's kinetic energy. This is due to the conservation of energy principle. The conservation of energy states that energy can neither be created nor destroyed, only transferred or transformed from one form to another.
In the context of the moving charged particle, the kinetic energy is given by the equation:
K = (1/2)mv^2
Where:
K is the kinetic energy of the particle,
m is the mass of the particle,
v is the velocity of the particle.
Since the magnetic force does not do any work on the particle, meaning it does not transfer energy to or from the particle, the kinetic energy of the particle remains constant. The magnetic force only changes the direction of the particle's motion without affecting its speed or energy.