If there was a way to accelerate a spaceship close to the speed of light to go visit some neighboring star system,
one would still face the problem that every particle the spaceship finds on its way will be a projectile hitting it
with almost the speed of light, causing radiation exposure and a lot of damage on the long run.
Assume that the spaceship can illuminate the space in front of it with a powerful laser that strips away the
electrons from any particle, transforming any matter in a collection of free electrons and of charged positive
particles.
Assume farther that the spaceship has technology that allows it to create a large magnetic field in front of
it. For this problem, assume that the spaceship is 100 m wide, that it moves at a speed of 107 m/s, and that the
magnetic field in front of it is also 100 wide but extends 1000 m in front of it with a (homogenous) magnitude
of 10−4 T.
1. What should be the orientation of the magnetic field at the front of the ship to effectively protect it during
its interstellar travel?
2. Once properly oriented, from which particles will this “magnetic shield” most effectively protect? The
electrons or the other positive particles?
3. Starting from which mass will some particles be able to hit the spaceship? (You will need to think about
what happens, make some drawings, and do the math in order to answer this question.)
4. Can the spaceship be protected from hydrogen atoms found in interstellar space?
To answer these questions, we need to understand the physics behind charged particles and magnetic fields. Let's break down each question and explain how to approach it:
1. What should be the orientation of the magnetic field at the front of the ship to effectively protect it during its interstellar travel?
To effectively protect the spaceship, the magnetic field should be perpendicular to the direction of motion. This means that the magnetic field lines should be parallel to the spaceship's velocity vector. This orientation will cause the charged particles to experience a force called the Lorentz force, which will divert them around the spaceship rather than allowing them to collide with it.
2. Once properly oriented, from which particles will this "magnetic shield" most effectively protect? The electrons or the other positive particles?
The Lorentz force depends on the charge and velocity of the particles. Since electrons have a smaller mass compared to other particles, they are more easily deflected by the magnetic field. Therefore, the magnetic shield will most effectively protect the spaceship from incoming electrons.
3. Starting from which mass will some particles be able to hit the spaceship?
To determine the mass at which particles can hit the spaceship, we need to consider the balance between the magnetic force and the force of gravity on the charged particles. Assuming the spaceship's magnetic field has been properly oriented, the magnetic force will deflect a charged particle if it is greater than or equal to the gravitational force acting on the particle.
The force of gravity on a charged particle is given by:
F_gravity = m * g
where m is the mass of the particle and g is the acceleration due to gravity. The magnetic force on a charged particle moving in a magnetic field is given by:
F_magnetic = q * v * B
where q is the charge of the particle, v is the velocity of the particle, and B is the magnitude of the magnetic field.
To determine the mass at which the magnetic force is equal to the gravitational force, we can set F_magnetic equal to F_gravity:
q * v * B = m * g
Solving for m:
m = (q * v * B) / g
This equation tells us the minimum mass at which particles will be deflected by the spaceship's magnetic shield. Particles with masses greater than this value will be able to hit the spaceship.
4. Can the spaceship be protected from hydrogen atoms found in interstellar space?
Hydrogen atoms are composed of a single proton and one electron, so they are positively charged particles. Since the magnetic shield is oriented to protect against electrons, it will not be as effective in deflecting positively charged particles like hydrogen atoms. Therefore, the spaceship may not be fully protected from hydrogen atoms found in interstellar space.
Remember, these explanations provide a general understanding of the concepts involved. Calculations and more detailed analysis may be necessary to obtain precise answers.