Nuclear Physics is the study of the nucleus of an atom. It includes studying the structure of the nucleus and the interactions of the particles constituting the nucleus.
The nucleus is the positively charged core of the atom around which the electron cloud is present. It has as its constituents the neutral neutrons and the positively charged protons. Collectively, neutrons and protons are called nucleons. Nuclear physics studies these particles and the way they are arranged inside the nucleus and the various interactions that they have with each other and the various processes that they undergo.
A natural question comes to the mind - since the protons are similarly charged and hence repel each other, and the neutrons are neutral and feel no electric force, what keeps these particles together in the nucleus? The answer is that besides the electrostatic force of repulsion between the positively charged protons, there is a very strong force of attraction between any two nucleons, irrespective of whether they are neutrons or protons that helps these particles bind together to form the compact nucleus.
This force is known as the nuclear force and is very strong, stronger than the electrostatic force. But this nuclear force is very short ranged. It is experienced by the nucleons which are very close to each other (of the order of 1 fm or a femtometre or 10-15m), and falls off rapidly with distance.
This force is important for considering the nuclear phenomena, for explaining the structure of the nucleus and stability of the nucleus.
Nuclear Physcis finds many applications in physics as well in technology. Nuclear energy generation through the process of nuclear fission is a growing field in power generation. It has medical applications that use the phenomena of radioactivity. It has applications in chemistry to find out the structure of molecules by the method of Nuclear Magnetic Resonance Spectroscopy or NMR Spectroscopy.