We don't know ...
but the theory goes that the 3 quarks that make up a proton set the values.
Positively charged protons, neutral neutrons and negatively charged electrons
Electrical charges are conserved, meaning that any net electrical charge was present since the beginning of the Universe. I would expect the net electrical charge of the Universe to be zero; it is also possible to get electrical charges by separation of charges. That is, if you have a charge of 0, you can separate it into a charge of +1 and a charge of -1; the sum of the two charges is still zero.
Atoms of the same kind. To be more precise, all atoms in an element have the same number of protons (but not necessarily the same number of neutrons - do some reading on "isotopes" for more details).
The nucleus of an atom is made up of neutrons and protons. Neutrons are neutral and protons have a positive charge so the nucleus is positively charged. Around the nucleus there are orbiting electrons which are negatively charged. The positive nucleus and the negative electrons make the overall charge of the atom neutral
Test charge is always a test charge. The electric field does not depend on the test charge. Usually we assume the test charge to be one coulomb positive charge. Though you make it half, it would never affect the field around the primary charge
Positively charged protons, neutral neutrons and negatively charged electrons
Protons and electrons are linked numerically; in any atom the number of protons and electrons is the same eg in carbon there are six of each. They have equal and opposite electric charges in an atom. The negative charge of each electron exactly balances the positive charge of each proton.
Atoms contain protons, neutrons and electrons; protons and neutrons are formed from quarks and gluons. A proton has an electric charge of +1; or 1,602176565(35)×10−19 Coulombs.
Electrons are negatively charged, smaller than neutrons and protons, and orbit around the nucleus. Neutrons have no charge, are about the same size as protons and are found in the nucleus. Protons have a positive charge, are about the same size as neutrons and are found in the nucleus.
The center of an atom is made up of two particles: protons and neutrons. Protons have a positive electric charge, while neutrons have no charge. Together, they make up the nucleus of an atom.
Electrical charges are conserved, meaning that any net electrical charge was present since the beginning of the Universe. I would expect the net electrical charge of the Universe to be zero; it is also possible to get electrical charges by separation of charges. That is, if you have a charge of 0, you can separate it into a charge of +1 and a charge of -1; the sum of the two charges is still zero.
Protons have positive charge, electrons have negative charge, and neutrons have no charge. The heavier particles, protons and neutrons, make up the atomic nucleus, which always has a positive charge.
Neutrons were discovered last, probably due to the lack of an electric charge. An electric charge would make the neutron more obvious for a variety of experiments.
Atoms of the same kind. To be more precise, all atoms in an element have the same number of protons (but not necessarily the same number of neutrons - do some reading on "isotopes" for more details).
Protons have positive charge, electrons have negative charge, and neutrons have no charge. The heavier particles, protons and neutrons, make up the atomic nucleus, which always has a positive charge.
Yes, neutrons help make up the nucleus of an atom along with protons. Neutrons have no charge, unlike protons which have a positive charge. Together, neutrons and protons are responsible for the mass of the nucleus.
A beta particle is an electron, and electrons are negative. You're probably thinking of a positron, which has the same mass as an electron but the opposite charge.