Let's analyze each statement one by one:
A. When the proton enters the fields, the magnitude of magnetic force on it is ten times the magnitude of electric force.
This statement is True. The magnetic force on a charged particle moving through a magnetic field is given by the equation Fm = qvB, and the electric force is given by Fe = qE. Given that the magnetic field is 10^-2 T and the electric field is 10 V/m, the ratio of the magnetic force to the electric force is (qvB)/(qE) = (vB)/E = (10^4)*(10^-2)/(10) = 10. Therefore, the magnetic force is indeed ten times the magnitude of the electric force.
B. The initial acceleration of the proton is in the y-z plane, at 84 degrees to the z-axis and at 6 degrees to the negative y-axis.
This statement is False. The proton experiences a force in the y-direction due to the magnetic field, but it also experiences a force in the x-direction due to the electric field. Therefore, the proton will accelerate in both the y and x directions, meaning its initial acceleration cannot be in the y-z plane alone.
C. When the proton enters the fields, the magnetic force on it is perpendicular to the electric field.
This statement is False. The magnetic force on the proton is given by the equation Fm = qvB, where v is the velocity of the proton and B is the magnetic field. Since v is in the positive x-direction and B is in the z-direction, the cross product of v and B will be in the negative y-direction. Therefore, the magnetic force is perpendicular to both the electric field and the proton's velocity.
D. The electric force on the proton is constant.
This statement is True. The electric force on a charged particle in a uniform electric field is constant, as long as the electric field remains constant.
E. The magnetic force on the proton is constant.
This statement is False. The magnetic force on a charged particle in a magnetic field depends on the velocity of the particle. Since the velocity of the proton is constant in this scenario, the magnetic force on the proton will also be constant.
F. The speed of the proton changes with time.
This statement is False. The speed of the proton, given as 10^4 m/s, remains constant throughout its motion. The forces acting on the proton only change its direction but do not affect its speed.
G. The path of the proton is a uniform helix.
This statement is True. When a charged particle moves through both an electric and magnetic field, it follows a curved path known as a helix. The path is helical because the magnetic force causes the particle to move in a circular path, while the electric force causes it to move along the z-axis. Thus, the path of the proton will indeed be a uniform helix.