28. Magnetic Fields and Forces
Circular Motion of Charges in Magnetic Fields
28. Magnetic Fields and Forces Circular Motion of Charges in Magnetic Fields
9PRACTICE PROBLEM
It has been demonstrated that when charged particles move in circular paths, they emit electromagnetic waves known as cyclotron radiation. Consequently, particles engaged in cyclotron motion with a velocity v experience a gradual depletion of their kinetic energy at a specific rate given by dk/dt = -(µ0•q4•B2•v2)/(8π•m2c). Considering a magnetic field strength of 3.0 T, determine the time it takes for (i) an electron and (ii) a proton to emit one-third of their energy while undergoing spiral motion due to the radiation.
It has been demonstrated that when charged particles move in circular paths, they emit electromagnetic waves known as cyclotron radiation. Consequently, particles engaged in cyclotron motion with a velocity v experience a gradual depletion of their kinetic energy at a specific rate given by dk/dt = -(µ0•q4•B2•v2)/(8π•m2c). Considering a magnetic field strength of 3.0 T, determine the time it takes for (i) an electron and (ii) a proton to emit one-third of their energy while undergoing spiral motion due to the radiation.