question_answer

The electric field E due to a point charge F at any point is defined as\[\underset{q\to 0}{\mathop{\lim }}\,\frac{F}{q},\] where\[q\] is the test charge and F is the force acting on it. What is the physical significance of \[\underset{q\to 0}{\mathop{\lim }}\,\] in this field expression?  Draw the electric lines of a point charge \[\mathbf{Q}\] when (i) \[\mathbf{Q>0}\] and(ii) \[\mathbf{Q}<\mathbf{0}.\]                                               

Answer:

                The \[\underset{q\to 0}{\mathop{\lim }}\,\] indicates that the test charge\[q\] is  small enough so that its presence does not affect the distribution of source and hence does change the value of electric field which we wish to measure. For electric lines of force of point charge Q, see Fig. (a) and Fig. (b)