Finding value of unknown charge

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

For this problem,

The solution is,

However, why did they assume that the electric field produced by charge q is always pointing to the left at the origin?

Many thanks!

 

[SammyS]

Homework Statement:: Please see below
Relevant Equations:: Please see below

For this problem,
View attachment 320613
The solution is,
View attachment 320612
However, why did they assume that the electric field produced by charge q is always pointing to the left at the origin?

Many thanks!

They are not assuming that the electric field is pointing to the left.

Think about it.

If $q$ is a positive charge, then indeed, the electric field at the origin, due to $q$, is to the left (negative).

What if $q$ is negative? Then you have a negative number multiplied by a negative number. In what direction is the electric field, due to $q$, pointing in this case?

 

[ChiralSuperfields]

They are not assuming that the electric field is pointing to the left.

Think about it.

If $q$ is a positive charge, then indeed, the electric field at the origin, due to $q$, is to the left (negative).

What if $q$ is negative? Then you have a negative number multiplied by a negative number. In what direction is the electric field, due to $q$, pointing in this case?

Thank you for your reply @SammyS !

If $q$ is negative, then the electric field due to the charge will be pointing to the right as a positive test charge would be attracted to the negative charge.