Question

Two point charges 4q and – q are placed at some distance. What fraction of field lines originating from 4q will terminate to – q. [Assume absence of any other charge in space] ​

Answer 1

Given:

Two point charges 4q and – q are placed at some distance.

To find:

Fraction of field lines emerging from 4q which will terminate to -q.

Calculation:

We know that number of field lines originating or terminating is directly proportional to the magnitude of the charge.

So, let number of field lines emerging from 4q be m.

$\therefore \: m \: \propto \: 4q$

$= > \: m = k \times 4q$

Let k be a constant.

Let number of Electrostatic field lines terminating at -q be n.

$\therefore \: n \: \propto \: q$

$= > \: n = k \times q$

So, fraction of Electrostatic field lines terminating at -q will be :

$\sf{frac. of \: field \: lines= \dfrac{n}{m} }$

$\sf{ = > frac. of \: field \: lines= \dfrac{k \times q}{k \times 4q} }$

$\sf{ = > frac. of \: field \: lines= \dfrac{ \cancel{k} \times \cancel{q}}{ \cancel{k} \times 4 \cancel{q}} }$

$\sf{ = > frac. of \: field \: lines= \dfrac{1}{4}}$

So, final answer is :

$\boxed{ \green{ \rm{ frac. of \: field \: lines= \dfrac{1}{4}}}}$