Question

T two point charges of 20 microcoulomb and 80 microcoulomb are 18 cm apart find the position where the electric field is zero

Answer 1

Given:

Two point charges of 20 microcoulomb and 80 microcoulomb are 18 cm apart.

To find:

Position where the electric field intensity is zero.

Calculation:

The position where the electric field intensity is zero is also known as the neutral point because the electric field intensity due to both the charges shall nullify each other at that point.

Let the point be located x units from 20 micro-C charge and (18 - x) unit from 80 micro-C charge.

$\therefore \: E1 = E2$

$= > \dfrac{k \times (20 \times {10}^{ - 6} )}{ {x}^{2} } = \dfrac{k \times (80 \times {10}^{ - 6}) }{ {(18 - x)}^{2} }$

Cancelling common terms :

$= > \dfrac{2}{ {x}^{2} } = \dfrac{8}{ {(18 - x)}^{2} }$

$= > \dfrac{ {(18 - x)}^{2} }{ {x}^{2} } = \dfrac{8}{2} = 4$

$= > \dfrac{18 - x}{x} = \sqrt{4} = 2$

$= > 2x = 18 - x$

$= > 3x = 18$

$= > x = 6 \: cm$

So the point is located 6 cm from 20 micro C charge and 12cm from 80 micro C charge.