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

Obviously, C, D, is true, E is true if one ignores direction of force, F is true (as the E field accelerates the proton), and since perpendicular speed is constant, G is true. Gee, it turned out easy.

think out G.

To determine which of the statements are false, we need to analyze the given information and apply the relevant physics principles. Let's break down each statement and explain how to get the answer:

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 verify this statement, we need to calculate both forces on the proton and compare their magnitudes. The electric force (F_e) on a charged particle moving in an electric field is given by F_e = qE, where q is the charge and E is the electric field. The magnetic force (F_b) on a charged particle moving in a magnetic field is given by F_b = qvB, where v is the velocity of the particle and B is the magnetic field. In this case, the fields are parallel, so we can ignore the vector components.

Since the magnitude of the electric field (E) is given as 10 V/m and the velocity of the proton (v) is given as 10^4 m/s, we can calculate the magnitudes of both forces using the given charge of a proton (q = 1.6 x 10^-19 C) and magnetic field strength (B = 10^-2 T).

Magnitude of electric force (F_e) = (1.6 x 10^-19 C) x (10 V/m)
Magnitude of magnetic force (F_b) = (1.6 x 10^-19 C) x (10^4 m/s) x (10^-2 T)

Upon calculating, we find that F_e is equal to F_b, not ten times larger. Therefore, statement A is false.

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 find the initial acceleration, we can use the Lorentz force equation, which describes the combined effect of electric and magnetic forces on a charged particle. The equation is F_net = q(E + v x B), where x represents the cross product.

Since the electric field (E) and magnetic field (B) are both in the z-direction (parallel to each other), the cross product term will only have components in the y-direction. The y-component of the cross product can be calculated as |v| |B| sinθ, where θ is the angle between v and B. In this case, the angle is not specified, so we cannot determine the initial acceleration direction. Therefore, statement B is false.

C. When the proton enters the fields, the magnetic force on it is perpendicular to the electric field.

Given that the magnetic field (B) and the electric field (E) are both parallel and in the z-direction, the magnetic force (F_b) on the proton will also be in the z-direction. This means it is parallel to the electric field, not perpendicular. Therefore, statement C is false.

D. The electric force on the proton is constant.

Since the electric field (E) is uniform and the charge (q) of the proton remains constant, the electric force (F_e) experienced by the proton will be constant. Therefore, statement D is true.

E. The magnetic force on the proton is constant.

Similarly, since the magnetic field (B) is also uniform, the velocity (v) of the proton remains constant, and the charge (q) is constant, the magnetic force (F_b) experienced by the proton will also be constant. Therefore, statement E is true.

F. The speed of the proton changes with time.

The speed of the proton can change with time if there is an acceleration acting on it. In this case, the initial acceleration was not determined. However, since the magnetic force (F_b) is perpendicular to the velocity (v) of the proton, it does not contribute to any speed changes. Therefore, the only force affecting the speed of the proton would be the electric force (F_e). As mentioned earlier, the electric force is constant and does not cause any change in speed. Therefore, statement F is false.

G. The path of the proton is a uniform helix.

To determine the path of the proton, we need to consider the combined effect of the electric and magnetic forces. If both forces are present and non-zero, the path of the proton will be curved in the xy-plane due to the Lorentz force acting on it. However, the given statements do not provide sufficient information to determine whether the path is a uniform helix. Therefore, statement G cannot be determined.

In summary, statements A, B, C, and F are false. Statements D and E are true. Statement G cannot be determined.