For an electric field passing through a flat surface perpendicular to it, the electric flux of the electric field through the surface is the product of the electric field's strength and the area of the surface. A certain flat surface consists of two adjacent squares, where the side length, in meters, of the larger square is $2$ times the side length, in meters, of the smaller square. An electric field with strength $35.00$ volts per meter passes uniformly through this surface, which is perpendicular to the electric field. If the total electric flux of the electric field through this surface is $2,800$ volts $\cdot$ meters, what is the electric flux, in volts $\cdot$ meters, of the electric field through the smaller square?