[hamdani yusuf (OP)]

If electrons are continuously shot into a black hole (from beta radiation or electron gun), will it be electrically charged?
Can the charge be sensed from outside, i.e. the Coulomb force?
How does the black hole mass affect the strength of Coulomb force, by modifying the distance from an outside object?

[Kryptid]

If electrons are continuously shot into a black hole (from beta radiation or electron gun), will it be electrically charged?

Yep. That's conservation of electric charge. There is an upper limit of the amount of charge that a black hole can carry (for a given mass, that is), though. For reasons that I do not understand, adding electric charge to a black hole causes the formation of an inner horizon in addition to the outer event horizon. As more charge is added, those two horizons get closer together in size. If the charge was sufficiently large, the horizons would merge (canceling each other out) and you'd end up with a naked singularity. Creating a naked singularity is currently thought to be impossible by general scientific consensus.

Can the charge be sensed from outside, i.e. the Coulomb force?

Yes. That's actually the mechanism that prevents a black hole from becoming "over-charged" and creating a naked singularity. As the black hole becomes more charged, the repulsive force makes it more and more difficult to add extra charge to the hole. In order to overcome that repulsion, the charged particles must be injected with increasingly high energy. Since that energy is the same as mass to a black hole, the black hole's mass also increases along with its charge.

How does the black hole mass affect the strength of Coulomb force, by modifying the distance from an outside object?

I have to admit, I don't know the answer to that one.

[hamdani yusuf (OP)]

If the electron gun shot at the black hole is swapped with a positron gun periodically, say every 1 hour, would it mean that the electric charge of the black hole a triangle wave?
Would it make the black hole emit electromagnetic radiation?

[paul cotter]

Adding alternate charge would indeed give rise to a sawtooth potential. However the basic principle of a black hole is that the gravitation is so strong that the escape velocity needed for anything to leave is above c, the speed of light in vacuo and hence nothing, including any form of electromagnetic radiation can emanate. You would have a hard job trying to see the sawtooth waveform as your scope probe would be sucked in!

[hamdani yusuf (OP)]

Adding alternate charge would indeed give rise to a sawtooth potential. However the basic principle of a black hole is that the gravitation is so strong that the escape velocity needed for anything to leave is above c, the speed of light in vacuo and hence nothing, including any form of electromagnetic radiation can emanate. You would have a hard job trying to see the sawtooth waveform as your scope probe would be sucked in!

How hard it would be is not my concern, at least for now. Is it possible though, at least in principle? 
I've watched a physics video saying that if the sun somehow turns into a black hole without changing its mass, the earth will stay in its current orbit.

[alancalverd]

Perfectly reasonable. The earth's orbit is determined by the mass of the sun, which didn't change. But the fate of anything approaching or attempting to leave the sun depends on its density, which would be very large for a black hole.