Question

Is FIGURE Q27.4 a possible surface charge distribution for a current-carrying wire? If so, in which direction is the current? If not, why not?

Short answer

No, in the wire, there is no net electric field.

Step-by-step solution

Concept Introduction 

The net electric field is the vector sum of the electric forces encountered by a particular charge when it encounters two or more interactions.

Explanation 

A positive ring is at a distance from the electric field.

The resultant electric field of ${\overrightarrow{E}}_1$and ${\overrightarrow{E}}_2$is ${\overrightarrow{E}}_{\text{net}}$which is along positive $x-$axis.

The resultant electric field of 2 and 3 charged rings is zero.

The resultant electric field of ${\overrightarrow{E}}_3$and ${\overrightarrow{E}}_4$is ${\overrightarrow{E}}_{\text{net}}^{\text{'}}$which is along negative $x-$axis.

Finally the resultant of ${\overrightarrow{E}}_{\text{net}}$and ${\overrightarrow{E}}_{\text{net}}^{\text{'}}$is zero.

Final Answer

So the internal electric field in the current carrying wire is zero. So no current flows through the wire.