Force Fields - Part II

There will be a force of repulsion between the charges and is again given by the inverse square law.

F      (q₁ q₂)
             
                   r²

or   F   =  +  1        (q₁ q₂)
                         
                              r² 

The force is repulsive and is indicated by a positive sign. 

   1         is a constant and is equal to 9 x 10⁹ N.m²/C²
        
  

The force in a vector form is expressed as 

                             
 F   = +   1        (q₁ q₂)      r
                 
                         r³ 

The force acts along the line joining the two charges.

This is known as the Coulombís Law or Coulombís inverse square law. Coulombís law states that the electric force between two charges is directly proportional to the charges and inversely proportional to the square of their distance.

If the charges are + q₁ and ñq₂, the force F would have a negative sign, indicating that it is an attractive force.

Just like the gravitational charges, electric charges also a exert field of force around themselves. In case of gravitational force field, the direction is always attractive, that is towards the mass. In case of electric charges, the force field can be either attractive or repulsive. The direction of the lines of force will be away from the charge in case of a repulsive force field.. The properties of the gravitational field and electric field are similar: closer the lines of force, stronger the intensity of the field.

3. Types of Force Fields
We have seen in our discussion above that there are at least two types of forces or force fields : gravitational and electrical. In Physics electricity and magnetism are two sides of the same coin : a moving charge generates magnetic field and vice versa [1]. Thus electrical forces are generalized as electromagnetic forces. 

The force that holds the nuclei together is called the nuclear force. Nuclei are made up of positively charged protons and electrically neutral neutrons tightly bound together within a distance of 10^-15 m. Now you may wonder as to why donít the protons fly apart due to electric repulsion? According to Coulombís law, they should. The nuclear force that is cementing the protons and neutrons together must be much more powerful than the Coulombís repulsive force. This force is called the nuclear force. This force is also called the strong force. An important feature of this force is that it acts at a very short range ~ 10^-15 m only. Beyond this range, the force rapidly falls off to zero. Also this force is independent of charge and acts on both the protons and neutrons equally. Thus the nuclear force is strong and short range. 

Table below gives the relative strengths of the different forces or force field.  

This indicates that if the magnitude of the gravitational  force is taken as 1, then electromagnetic force is 10³⁸ times stronger; the nuclear force is 10⁴⁰ times stronger. 

There is a fourth force in nature called the weak force. It is at least a billion times weaker than the nuclear force and is observed only in a beta decay of radioactive nuclei.

Both gravitational and electromagnetic forces are long range forces, but the nuclear and weak forces are short range forces.

[1] A detailed explanation for this is beyond the syllabus.

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