Monday, November 19, 2012

Coulomb’s Law In Vector Form

Let the position vectors of charges q1 and q2 be r1 and r2 respectively Fig. We denote force on q1 due to q2 by F12 and force on q2 due to q1 by F21. The two point charges q1 and q2 have been numbered 1 and 2 for convenience and the vector leading from 1 to 2 is denoted by r21:
 r21 = r2 r1.  In the same way, the vector leading from 2 to 1 is denoted by r12: r12 = r1 r2 = – r21 .The magnitude of the vectors r21 and r12 is denoted by r21 and r12, respectively (r12 = r21). The direction of a vector is specified by a unit vector along the vector. To denote the direction from 1 to 2 (or from 2 to 1), we define the unit vectors:
Coulomb’s force law between two point charges q1 and q2 located at r1 and r2 is then expressed as
If q­1 and q2 are of the same sign (either both positive and both negative), F21 is along ˆr 21, which denotes repulsion, as it should be for like charges. If q1 and q2 are of opposite signs, F21 is along – ˆr 21(= ˆr 12), which denotes attraction, as expected for unlike charges.

Thus, we do not have to write separate equations for the cases of like and unlike charges.  The force F12 on charge q1 due to charge q2, is obtained from force F21, by simply interchanging 1 and 2, i.e.
Thus, Coulomb’s law agrees with the Newton’s third law.

Some of these questions which may be asked in your Board Examination 2012-2013

Q1: When a plastic comb is passed through dry hair, what type of charge is acquire by comb?

Q2: Does motion of a body affect its charge

What is the origin of frictional forces

Answer these questions in comment box and help your friends


  1. the comb should accquire a negative charge because your hair has a natural tendency to give up electrons charge on a body does not change with motion of the body

  2. 1. positives (+ev) 2.yes, more motions more charges 3. From the surface of the rubbing body

  3. how this r sq. inverse proportionality is proved theoritically

  4. if charge depends on mass and mass changes with motion then why charge does not change with motion...

  5. Since our body has a high no of protons and electrons its has a tendency to gain the electrons and the charge passes on to the earth and thus comb acquires a positive charge.and attracts neutral small objects.

  6. Visit this blog for cool gizmos:

  7. This comment has been removed by the author.

  8. why we take r21 for the direction from q1 to q2. In some books for the direction of q1 to q2 they simply took r12 as a unit vector. Please tell me what should we take as an unit vector