Question

What is the negative charge if the electric field at the dot is zero?

Answer 1

-4 Q

Step-by-step explanation:

We are given that

Positive charge=+Q

Let the distance between positive charge and dot=r

The distance between negative charge q and dot=2r

We know that

Electric field,E=
`(KQ)/(r^2)`

Electric field due to positive charge=
`E_1=(KQ)/(r^2)` (outward direction)

Electric field due to negative charge q=
`E_2=(Kq)/((2r)^2)`(Inward direction)

The direction of E1 and E2 are opposite

According to question

`(KQ)/(r^2)-(Kq^2)/((2r)^2)=0`

`(KQ)/(r^2)=(Kq)/((2r)^2)`

`(q)/(4)=Q`

`q=4Q`

The charge q is negative therefore, q=-4 Q