Introduction:

When two protons move parallel to the x-axis in opposite directions with equal speed, they experience both magnetic and electric forces. The ratio of the magnetic force to the electric force acting on one of the protons can be determined by analyzing the properties of these forces.

Magnetic Force:

The magnetic force on a moving charged particle is given by the equation:

Fm = qvBsinθ

where Fm is the magnetic force, q is the charge of the particle, v is its velocity, B is the magnetic field, and θ is the angle between the velocity and the magnetic field.

Electric Force:

The electric force on a charged particle moving in an electric field is given by the equation:

Fe = qE

where Fe is the electric force, q is the charge of the particle, and E is the electric field strength.

Analysis:

In this scenario, the protons have equal speed v but move in opposite directions. Therefore, their velocities are in opposite directions as well.

The magnetic force experienced by proton A can be calculated using the equation mentioned earlier. Since the velocity of proton A is in the opposite direction to the magnetic field, the angle θ between them is 180 degrees. Thus, the magnetic force on proton A is:

Fm(A) = qvBsin180 = 0

As the magnetic force is zero, the ratio of the magnetic force to the electric force on proton A is also zero.

On the other hand, the electric force experienced by proton A can be calculated using the second equation mentioned earlier. Since there is no information given about an electric field, we cannot determine the exact value of the electric force. However, we can conclude that the electric force will not be zero unless the electric field is zero.

Conclusion:

In this scenario, the ratio of the magnetic force to the electric force acting on proton A is zero. This is because the magnetic force on proton A is zero due to the opposite direction of its velocity compared to the magnetic field. The electric force, however, will not be zero unless the electric field is zero.