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www.GOALias.blogspot.comPhysicsFIGURE 1.12 Electric field at apoint due to a system of charges isthe vector sum of the electric fieldsat the point due to individualcharges.Electric field E 1at r due to q 1at r 1is given by1 q1E 1= rˆ24πεr0 1P1Pwhere ˆr 1Pis a unit vector in the direction from q 1to P,and r 1Pis the distance between q 1and P.In the same manner, electric field E 2at r due to q 2atr 2isE 2=14πεq22r0 2Prˆ2Pwhere ˆr 2P is a unit vector in the direction from q 2to Pand r 2Pis the distance between q 2and P. Similarexpressions hold good for fields E 3, E 4, ..., E ndue tocharges q 3, q 4, ..., q n.By the superposition principle, the electric field E at rdue to the system of charges is (as shown in Fig. 1.12)E(r) = E 1(r) + E 2(r) + … + E n(r)1 q1 1 q21 qn= rˆ + rˆ + ... + rˆ2 2 24πε r 4πε r 4πεr1P 2P nP0 1P 0 2P 0 nP20E(r)=14qni∑ r ˆ2 iP(1.10)πε 0 i = 1 riPE is a vector quantity that varies from one point to another point in spaceand is determined from the positions of the source charges.1.8.2 Physical significance of electric fieldYou may wonder why the notion of electric field has been introducedhere at all. After all, for any system of charges, the measurable quantityis the force on a charge which can be directly determined using Coulomb’slaw and the superposition principle [Eq. (1.5)]. Why then introduce thisintermediate quantity called the electric field?For electrostatics, the concept of electric field is convenient, but notreally necessary. Electric field is an elegant way of characterising theelectrical environment of a system of charges. Electric field at a point inthe space around a system of charges tells you the force a unit positivetest charge would experience if placed at that point (without disturbingthe system). Electric field is a characteristic of the system of charges andis independent of the test charge that you place at a point to determinethe field. The term field in physics generally refers to a quantity that isdefined at every point in space and may vary from point to point. Electricfield is a vector field, since force is a vector quantity.The true physical significance of the concept of electric field, however,emerges only when we go beyond electrostatics and deal with timedependentelectromagnetic phenomena. Suppose we consider the forcebetween two distant charges q 1, q 2in accelerated motion. Now the greatestspeed with which a signal or information can go from one point to anotheris c, the speed of light. Thus, the effect of any motion of q 1on q 2cannot