Fundamental Forces of Nature Prepared by; Dr. Rajesh Sharma Assistant Professor Dept of Physics P.G.G.C-11, Chandigarh Email: drrajeshsharma@in.com

Fundamental Forces

Exchange Forces All four of the fundamental forces involve the exchange of one or more particles. Even the underlying color force which is presumed to hold the quarks together to make up the range of observed particles involves an exchange of particles labeled gluons. Such exchange forces may be either attractive or repulsive, but are limited in range by the nature of the exchange force. The maximum range of an exchange force is dictated by the uncertainty principle since the particles involved are created and exist only in the exchange process - they are called "virtual" particles. The relative strength of these forces ranges as FORCE EXCHANGE PARTICLE Strong Force gluon Electromagnetic Force Photon Weak Force W and Z Gravity graviton

The Strong Force A force which can hold a nucleus together against the enormous forces of repulsion of the protons is strong indeed. However, it is not an inverse square force like the electromagnetic force and it has a very short range. Yukawa modeled the strong force as an exchange force in which the exchange particles are pions and other heavier particles. The range of a particle exchange force is limited by the uncertainty principle. It is the strongest of the four fundamental forces

The Electromagnetic Force One of the four fundamental forces, the electromagnetic force manifests itself through the forces between charges (Coulomb's Law) and the magnetic force, both of which are summarized in the Lorentz force law. Fundamentally, both magnetic and electric forces are manifestations of an exchange force involving the exchange of photons . The quantum approach to the electromagnetic force is called quantum electrodynamics or QED. The electromagnetic force is a force of infinite range which obeys the inverse square law, and is of the same form as the gravity force.

The electromagnetic force holds atoms and molecules together The electromagnetic force holds atoms and molecules together. In fact, the forces of electric attraction and repulsion of electric charges are so dominant over the other three fundamental forces that they can be considered to be negligible as determiners of atomic and molecular structure. Even magnetic effects are usually apparent only at high resolutions, and as small corrections.

The Weak Force One of the four fundamental forces, the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z. Since the mass of these particles is on the order of 80 GeV, the uncertainty principle dictates a range of about 10-18meters which is about 0.1% of the diameter of a proton. The weak interaction changes one flavor of quark into another. It is crucial to the structure of the universe in that 1. The sun would not burn without it since the weak interaction causes the transmutation p -> n so that deuterium can form and deuterium fusion can take place. 2. It is necessary for the buildup of heavy nuclei. The role of the weak force in the transmutation of quarks makes it the interaction involved in many decays of nuclear particles which require a change of a quark from one flavor to another. It was in radioactive decay such as beta decay that the existence of the weak interaction was first revealed. The weak interaction is the only process in which a quark can change to another quark, or a lepton to another lepton - the so-called "flavor changes".

Central and Non-central Forces A force which is directed along the line joining the centre of the two interacting particles or bodies is called Central Force. Examples: The gravitational and Electrostatic forces A central force can be written as Where F(r) is the function of distance and represents the magnitude of the force. and is the unit vector representing the direction of the central force.

Inverse Square Law Forces Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound or radiation obey the inverse square law.

The magnitudes of the electrostatic and gravitational force between two point particles at rest is given by Where K is the constant, r is distance between two points. Such forces are inverse square law forces. Gravitational Interaction: For masses m1 and m2 we have (1) So, the gravitational force Electrostatic Interaction: For two charges q1 and q2 we have (2) So, the electrostatic force

Characteristics of central forces Act along the line joining the centres of the interacting particles. Conservative in nature i.e. the work done by these forces along a closed path is zero. Long range forces and effective for even large distances apart. Derivable from the scalar potential. Angular momentum is conserved. Obey inverse square law.

Center of Mass for Two Particles The center of mass is the point at which all the mass can be considered to be "concentrated" for the purpose for the purpose of calculating the "first moment", i.e., mass times distance. For two masses this distance is calculated from For the more general collection of N particles this becomes and when extended to three dimensions: This approach applies to discrete masses even if they are not point masses if the position xi is taken to be the position of the center of mass of the ith mass.

Continuous Distribution of Mass For a continuous distribution of mass, the expression for the center of mass of a collection of particles : becomes an infinite sum and is expressed in the form of an integral

For the case of a uniform rod this becomes This example of a uniform rod previews some common features about the process of finding the center of mass of a continuous body. Continuous mass distributions require calculus methods involving an integral over the mass of the object. Such integrals are typically transformed into spatial integrals by relating the mass to a distance, as with the linear density M/L of the rod. Exploiting symmetry can give much information: e.g., the center of mass will be on any rotational symmetry axis. The use of symmetry would tell you that the center of mass is at the geometric center of the rod without calculation.