Question

The Wayfinder’s™ propulsion system works by firing a beam of electrons behind it at 10MV. Another possible method for producing artificial gravity is to accelerate at 9.81m/s2 . This would mean, as long as the ship keeps accelerating, it would be like there was gravity. It would also eliminate the need for large electric fields on the ship.

a) To achieve an acceleration of 9.81m/s2 , what will the current of electrons be?

Answer 1

Since electrons are accelerated by 10MV, the velocity of the electrons will be, given by the energy balance equation,

..........EQ1

where, is the final velocity of the electrons

is the charge of an electron

is the mass of an electron

is the voltage for accelerating the electron

substituting in EQ1 we get,

Now the momentum of all the electrons in the beam will provide the momentum to the space ship. Thus, the force balance gives,

.....EQ2

where, is the mass of the space ship,

is the acceleration of the spaceship

is the number of electrons emitted per second

The current of the electron beam will be,

.......EQ3

Using EQ2 and substituting values in EQ3 we get

Note: we need the mass of the spaceship