A proton follows a spiral path througha gas in a magnetic field of .010 T , perpendicular to the plane of the spiral.In two successive loops, at point P and Q, the radii are 10.0mm and 8.5 mm,respectively.Calculate the change in Kinetic energy of the proton as it travels from P to Q.
To calculate the change in kinetic energy of the proton as it travels from point P to Q, we need to use the principle of conservation of energy. The magnetic field does not do any work on the proton, so the change in kinetic energy is solely due to the change in potential energy.
The potential energy of a charged particle moving in a uniform magnetic field is given by the equation:
U = -magnetic moment * magnetic field * cosine(theta)
In this case, since the proton is moving perpendicular to the magnetic field, the angle theta is 90 degrees. Therefore, the potential energy at point P is:
UP = -(magnetic moment * magnetic field) * cos(90) = 0
Similarly, the potential energy at point Q is:
UQ = -(magnetic moment * magnetic field) * cos(90) = 0
Since the potential energy is the same at both points P and Q, there is no change in potential energy. Therefore, the change in kinetic energy is also 0.
Hence, the change in kinetic energy of the proton as it travels from P to Q is 0.