Q:

Accelerated charges and electromagnetic fields

It is known that accelerated charged particles radiate electromagnetic waves.  
Now let's consider $2$ boxes $A$ and $B$ accelerated with the same acceleration $\vec{a}$ and with the same variable velocity $\vec{v_t}$. Let the box $A$ contain a charged particle of charge $q$. So $q$ will radiate electromagnetic waves.  

My question is:  

Will the box $B$ experience any electromagnetic effect due to the charge $q$ in box $A$?
  This question arose because the boxes have a null-relative velocity. 

This is not a homework question, a question that just arose in my mind while studying electromagnetic fields.   

A:

You are saying in the comments that you are asking about two electrons comoving.
It is very important to understand the difference between EM waves (radiation) and static EM field.

An electromagnetic field (also EMF or EM field) is a magnetic field produced by moving electrically charged objects.[1] It affects the behavior of non-comoving charged objects at any distance of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction.
  The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field.

https://en.wikipedia.org/wiki/Electromagnetic_field

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy.[1]
  Electromagnetic waves are emitted by electrically charged particles undergoing acceleration,[4][5] and these waves can subsequently interact with other charged particles, exerting force on them. EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact.

https://en.wikipedia.org/wiki/Electromagnetic_radiation
When the two boxes move together (they are stationary relative to each other) then the B box will not see Box A (electron) emit EM waves (radiation). It is because in B's frame A is stationary.
Now regardless of this, B electron will feel the static EM field of A electron, even when they are stationary relative to each other. The two electrons will repel.

