Question

Along the line connecting the two charges, at what distance from the charge q1 is the total electric field from the two charges zero? Express your answer in terms of some or all of the variables s, q1, q2 and k =14πϵ0

Answer 1

Answer:

Distance of zero electric field from charge q1 = $\frac{a\sqrt{q1}}{(\sqrt{{q2}}+\sqrt{q1})}$

Explanation:

let the distance between the charges be 'a'

and the point of equal electric field be at a distance 'x' from the charge q1

Given:

the charges as q1 and q2

we know that the Electric field (E) is given as

$E=\frac{kQ}{r^2}$

where,

k = Electric field constant

Q = charge

r = distance of the point from the charge where Electric field is being measures

⇒let the distance between the charges be 'a'

and the point of equal electric field be at a distance 'x' from the charge q1

⇒Now electric field due to the charges q1 = $E_1=\frac{kq1}{r_1^2}$

electric field due to the charges q2 = $E_1=\frac{kq2}{r_2^2}$

from the figure attached:  $r_1=x$ and $r_2=a-x$

for the electric field from the charges to be zero

$\frac{kq1}{r_1^2}=\frac{kq2}{r_2^2}$

substituting the values

$\frac{kq1}{a^2}=\frac{kq2}{(a-x)^2}$

or

$\frac{a-x}{x}=\sqrt{\frac{q2}{q1}}$

or

$\frac{a}{x}-\frac{x}{x}=\sqrt{\frac{q2}{q1}}$

or

$a=(\sqrt{\frac{q2}{q1}}+1)x$

or

$x = \frac{a}{(\sqrt{\frac{q2}{q1}}+1)}$

or

$x = \frac{a\sqrt{q1}}{(\sqrt{{q2}}+\sqrt{q1})}$