Question

Two charges $Q$ and $4Q$ are set on the line shown. The two charges create an electric field in the region around them.
At which point labeled on the line is the electric field zero?

• A. A
• B. B
• C. C
• D. D
• E. At no point is E = 0.

Answer 1

The correct option is B B

Let the electric field $E$ is zero at a point $P$ between the two given charges , at a distance $x$ from the charge $-Q$ , .

at point $P$, electric field due to $-Q$

$E_1=-KQ/x^2$

at point $P$, electric field due to $-4Q$ which is at a distance $d$ from $-Q$ ,

$E_2=-4KQ/(d-x{)}^2$

as $E_1$ and $E_2$ are in opposite direction due to two negaitive charges and electric field is zero at point $P$ , therefore

$E_1=E_2$

or $-KQ/x^2=-4KQ/(d-x{)}^2$

or $4x^2=(d-x{)}^2$

or $x=d/3$ or $x=-d$

but $x=-d$ is not possible as point $P$ is in between the two charges ,

therefore $x=d/3$ it is point B at which field is zero .

option B is correct.