A 2.3-keV proton is moving horizontally and passes perpendicular to the Earth’s magnetic field at a location where the field magnitude is 52.0 T.

i) Determine the magnetic force on the proton?

ii) Find the ratio of this force to the gravitation force on the proton?

iii) What energy of proton would be needed to make the magnetic and gravitational forces to be equal?

iv) What direction proton would be, to keep the motion in horizontal?

change the 2.3keV to velocity.

Then, force magnetic=Bq*veloctiy

I am uncertain what difficulty you are having here.

To answer these questions, we need to use the equation for the magnetic force on a moving charged particle:

F = q * v * B * sin(theta),

where:
- F is the magnetic force,
- q is the charge of the particle,
- v is the velocity of the particle,
- B is the magnetic field strength, and
- theta is the angle between the velocity vector and the magnetic field vector.

i) To determine the magnetic force on the proton, we need to know the charge of a proton. The charge of a proton is +1.6 x 10^-19 Coulombs. The velocity of the proton is not given in the question, so we cannot directly calculate the magnetic force.

ii) To find the ratio of the magnetic force to the gravitational force on the proton, we need to know the mass of the proton. The mass of a proton is approximately 1.67 x 10^-27 kg. The gravitational force on a proton can be calculated using the equation:

F_gravity = m * g,

where g is the acceleration due to gravity. On Earth, g is approximately 9.8 m/s^2. Once we have the magnetic force and gravitational force, we can calculate the ratio.

iii) To find the energy of the proton needed to make the magnetic and gravitational forces equal, we need to set the magnetic force equal to the gravitational force and solve for the proton's energy. This can be done by equating the equations for the magnetic force and gravitational force, and then solving for the kinetic energy of the proton.

iv) To determine the direction in which the proton would move to keep its motion horizontal, we need to find the angle between the velocity vector of the proton and the magnetic field vector. Since the proton is moving horizontally, perpendicular to the Earth's magnetic field, the angle between the velocity vector and magnetic field vector would be 90 degrees.

Note: The actual calculation of the values will require specific information from the question that is not provided, such as the velocity of the proton. You should use the specific given values to calculate the answers to the questions.