The following pictures depict electric field lines for various charge configurations.

(i) In figure (a) identify the signs of two charges and find the ratio `|(q_(1))/(q_(2))|`
(ii) In figure (b) calculate the ratio of two positive charges and identify teh strength of the electric field at three points A, B and C
(iii) Figure (c) represents the electric field lines for three charges . If `q_(2)` =-20nC then calculate the values of `q_(1)` and `q_(3)`

Explanation

(i) The electric field lines start at `q_(2)` and end at `q_(1)` . In figure (a) `q_(2)` is positive and `q_(1)` is negative . The number of lines starting from `q_(2)` is 18 and number of the lines ending at `q_(1)` is 6. So `q_(2)` has greater magnitud. The ratio of `|(q_(1))/(q_(2))|=(N_(1))/(N_(2))=(6)/(8)=(1)/(3)` . It implies that `|q_(2)|=3|q_(1)|`.
(ii) In figure (b) , the number of field lines emanating from both positive charges are equal (N=18). So the charges are equal . At point A the electric field line are denser compared to the lines at point B. So the electric at point A is greater in magnitude compared to the field at point B . Further no electric field line passes through C which implies that the resultant electric field at C due to these two charges is zero .
(iii) In the figure (c) the electric field lines start at `q_(1)` and `q_(3)` and end at `q_(2)` and end at `q_(2)` , This implies that `q_(1)` and `q_(3)` are positive charges. The ratio of the number of field lines is `|(q_(1))/(q_(2))|=(8)/(16)=|(q_(3))/(q_(2))|=(1)/(2)` implying that `q_(1)` and `q_(3)` are half of the magnitude of `q_(2)` . So `q_(1)=q_(3)=+10n` C .