A proton traveling at 10^4 m/s in the positive x-direction, enters a region where there is uniform electric field of magnitude 10 v/m and a uniform magnetic field of magnitude 10^-2 T. The electric and magnetic fields are parallel and are in the z-direction. In the following statements which of the two are false
A. When the proton enters the fields, the magnitude of magnetic force on it is ten times the magnitude of 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
C. When the proton enters the fields the magnetic force on it is perpendicular to the electric field
D. The electric force on the proton is constant
E. The magnetic force on the proton is constant
F. The speed of the proton changes with time
G. The path of the proton is a uniform helix
To determine which of the statements are false, let's analyze each statement one by one:
A. When the proton enters the fields, the magnitude of the magnetic force on it is ten times the magnitude of the electric force.
To calculate the magnitude of the electric force, we can use the equation F_e = qE, where q is the charge of the proton and E is the magnitude of the electric field. In this case, the electric force would be F_e = (1.6 x 10^-19 C)(10 V/m).
To calculate the magnitude of the magnetic force, we can use the equation F_m = qvB, where v is the velocity of the proton and B is the magnitude of the magnetic field. In this case, the magnetic force would be F_m = (1.6 x 10^-19 C)(10^4 m/s)(10^-2 T).
Comparing the two forces, we can find that F_m/F_e = [(1.6 x 10^-19 C)(10^4 m/s)(10^-2 T)] / [(1.6 x 10^-19 C)(10 V/m)]. After simplifying, we get F_m/F_e = 1000.
Since F_m/F_e is equal to 1000, statement A is false. The magnitude of the magnetic force is actually 1000 times greater than 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.
To determine the direction of the initial acceleration, we need to consider the cross product of the velocity of the proton with the magnetic field. As the velocity is in the positive x-direction, and the magnetic field is in the z-direction, the cross product will give us a vector pointing in the direction of the y-axis.
Since the y-axis and z-axis form a plane, the initial acceleration of the proton will be in the y-z plane. However, the specific angles stated in statement B are incorrect.
Therefore, statement B is false.
C. When the proton enters the fields, the magnetic force on it is perpendicular to the electric field.
Since the electric and magnetic fields are parallel and both in the z-direction, the magnetic force and electric field will be perpendicular to each other.
Therefore, statement C is true.
D. The electric force on the proton is constant.
The electric force on a charged particle in a uniform electric field is constant as long as the field remains constant and the particle doesn't change its position.
Therefore, statement D is true.
E. The magnetic force on the proton is constant.
The magnetic force on a charged particle in a uniform magnetic field is always perpendicular to both the particle's velocity and the magnetic field. In this case, since the proton's velocity is in the positive x-direction and the magnetic field is in the z-direction, the magnetic force will always be orthogonal to both.
Therefore, statement E is true.
F. The speed of the proton changes with time.
Since there is no force acting in the x-direction (assuming no other external forces), the proton will continue to move with a constant speed in the positive x-direction.
Therefore, statement F is false. The speed of the proton remains constant.
G. The path of the proton is a uniform helix.
Given the constant speed along the x-direction and the constant acceleration in the y-z plane due to the magnetic field, the path of the proton will be a helix.
Therefore, statement G is true.
In conclusion:
False statements: A, B, F
True statements: C, D, E, G