Acceleration of a proton/electron toward a neutron star

[Starkiller]

So, I have this scenario:

A neutron star with radius R = 13 km
Time for 1 rotation is 3,150807 ms, so frequency f about 317,379008 Herz
Mass 1,97 times the Sun's which is then 1,97*(1,9884*10^30) kg
Extra given information: the magnetic axis is aligned with its rotational axis (not that likely but okkkk)

Now this Neutron star is a magnetar and has a powerful magnetic field of about 10^14 Gauss

Now we are in a rocket and we fire a single electron toward its magnetic south pole
initial distance from N-star: 10 million km
initial velocity of electron upon firing: an underwhelming 50 m/s

As the electron approaches the magnetic south pole, what will happen with its acceleration?
How does one calculate its speed upon colliding and how big the impact force is?
If the speed becomes relativistic would this formula be correct: KE = mc^2-m0*c^2
I'm kind of looking as to how the gravity and electromagnetic forces would influence this electron, I assume if one fired it at its magnetic north pole it would be totally different.

So it starts off with a normal velocity and gravitational acceleration g = (-GM*r-accent)/r^2
and how does electromagnetic force work with/against this acceleration?
And if it reaches velocity 0,2c should the gamma factor get a play in the scenario?

Yeah well, is it rude to put such a text out without giving any solutions? I tried, though, but my notebook is messy and I'm sure I'm wronggggg. If not helping me out maybe at least say what's wrong in my reasoning and how I should start off please?

I'm fairly new, but I must admit I've been hanging around threads before, lurking from the dark.

All the best/thanks in advance I guesss,
Me,

 

[davenn]

As the electron approaches the magnetic south pole, what will happen with its acceleration?
How does one calculate its speed upon colliding and how big the impact force is?
If the speed becomes relativistic would this formula be correct: KE = mc^2-m0*c^2
I'm kind of looking as to how the gravity and electromagnetic forces would influence this electron, I assume if one fired it at its magnetic north pole it would be totally different.

do you know how a charged particle moves in a magnetic field ?
go have a search and read-up

then come back and consider how that may affect the situation

 

[Starkiller]

Okay so I drew the neutron star
and the vector of its magnetic field is like, from its magnetic North Pole to its magnetic South Pole
So if we have a proton
and we shoot it right toward its magnetic south pole, it will be attracted and the vector of the lorentzforce acting on it
is straight toward the neutron star (perpendicular on its surface)

Lortentzforce on charged particle = Bqv
But, the formula says that vector B must be perpendicular to vector V
what if they both point in the same direction?

But am I thinking into the right direction? anyone

 

[willem2]

Lortentzforce on charged particle = Bqv
But, the formula says that vector B must be perpendicular to vector V
what if they both point in the same direction?

But am I thinking into the right direction? anyone

you have lorentz force F = q(B x v) B and V are vectors and x stand for the cross product of two vectors. https://www.mathsisfun.com/algebra/vectors-cross-product.html The crossproduct is 0 if the vectors are in the same direction, so there will be no magnetic force if you shoot the electron towards the poles. You might want to consider some other way.

 

[davenn]

Okay so I drew the neutron star
and the vector of its magnetic field is like, from its magnetic North Pole to its magnetic South Pole
So if we have a proton
and we shoot it right toward its magnetic south pole, it will be attracted and the vector of the lorentzforce acting on it
is straight toward the neutron star (perpendicular on its surface)

no.
I was trying to get you to find what happens to a charged particle in a magnetic field.
So far you haven't answered that correctly

 

[Starkiller]

Hmmm I did some righthand rule stuff and I kinda couldn't find the perfect position where Fl and Fg are working in the exact same direction
I think its better to go with the Gravitational acceleration of the proton if shot at the pole, so we can leave out any Fl complications

Though it might be more fun with Fl...

 

[stefan r]

Hmmm I did some righthand rule stuff and I kinda couldn't find the perfect position where Fl and Fg are working in the exact same direction
I think its better to go with the Gravitational acceleration of the proton if shot at the pole, so we can leave out any Fl complications

Though it might be more fun with Fl...

If you are trying to ask about the effect of gravity on a particle the pole is a good question. If you are trying to understand the magnetic field look at the equator instead. Other angles make it more complicated.

In pulsars the magnetic field is not aligned with the pole. Consider what happens if the magnetic pole is on the equator and you shoot the proton down the rotational axis.

Auroras occur on both of Earth's poles, and other planets.
Tethers unlimited has electrodynamic tethers with diagrams.