3. When a steady current, I, is flowing through a conductor (e.g. the carbon paper here) with a non-negligible resistance, R, it will be possible to maintain a potential difference, AV=IR, between parts of the conductor along the direction of the current. Explain why in this situation there should be an electric field in the direction of the current but not in the direction perpendicular to the current. [1]

When a steady current, I, flows through a conductor with a non-negligible resistance, R, a potential difference, ΔV=IR, is maintained along the direction of the current. This is due to Ohm's law, which states that the potential difference across a conductor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance.

Now, an electric field is a region in space where an electric charge experiences a force. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is defined as the electric force per unit charge.

In the case of a current flowing through a conductor, the electric field is in the direction of the current. This is because the current is a flow of electric charges (in this case, electrons) that are moving due to the force exerted on them by the electric field. The direction of the electric field is therefore the same as the direction of the current.

However, there is no electric field in the direction perpendicular to the current. This is because the electric field is created by the potential difference, which is maintained along the direction of the current. There is no potential difference in the direction perpendicular to the current, so there is no electric field in that direction.

In other words, the electric field is always directed from regions of high potential to regions of low potential. Since the potential difference is along the direction of the current, the electric field is also in that direction, and not in the direction perpendicular to the current.