Final answer:
The left-hand surface of a solid gold cube in a uniform electric field directed from left to right would have a negative charge due to the motion of free electrons within the conductor, which move until the internal electric field is zero.
Step-by-step explanation:
In the presence of a uniform external electric field that is directed horizontally from left to right, a solid gold cube would experience a redistribution of its free charges. Due to the electric field, free charges in the gold (which are electrons) would move such that they would slightly accumulate on the surface opposite to the direction of the field. This would result in a negative charge on the left-hand surface of the cube, as electrons are negatively charged.
Gold, being a conductor, allows free movement of its charges. According to principles of electrostatics, the free charges within a conductor redistribute until the internal electric field is zero and the external electric field is perpendicular to its surface in electrostatic equilibrium. In this case, the mobile charges move to the surfaces of the cube to cancel out the external field within the gold.
The charge distribution is such that, when the cube is in electrostatic equilibrium, the surface facing the source of the electric field would have a higher concentration of mobile charges of opposite sign to the field, thus in our case, the left-hand surface of the cube, facing the source, would accumulate negative charge.