Energy density

Even the best batteries can only store 0.36 to 0.9 MJ/kg. Compare this with diesel that has an energy content of 41 MJ/kg. The difference is less if the efficiencies of the diesel motor and the electric car are considered. Lithium ion batteries has 0.9 MJ*85%/(41 MJ*40%)*100 = 4.7 % of the energy of the diesel car by volume [Wikipedia]. 
This means that one needs twenty times more batteries than diesel fuel to travel the same distance between refuelling/ charging. Actually, the batteries would need to be even bigger such that the overall weight of an automobile would increase due to the additional weight added by the batteries.

The figure shows schematic roads in a mesh with big and small roads. On the small roads, which constitute the major part of the roads, the vehicles run on batteries. On the big roads with more intense traffic and longer distances to be covered, the batteries are continually charged while driving.

Sweden has around 2,000 km European highways and county roads. If these roads were distributed evenly in a mesh over all Sweden the mesh size would be around 45 km squares. This is pretty much how the road system in Sweden looks like but the mesh size is smaller in the south of Sweden and sparser in the north where there is less population.

The battery cars would accordingly only have to be designed to drive within one square of the mesh. This is an acceptable and manageable requirement.  Battery cars can meet this requirement already today. A distance of 100 km would give a good margin of error. Within one square it could also be possible to charge the vehicle from the grid, for instance at a summerhouse. The time for charging would be longer, but that would not be a problem as it could be done overnight or while parking for a meeting or other stop. 
When driving long distances the norm is to use big roads.  If we have a system where the larger roads are electrified it will actually be better than today’s system. An electric car would then be able to drive from the north of Norway to the south of Spain without stopping for refuelling or charging. 

Optimizing the mesh

The optimal size of the mesh depends on the cost of electrifying the road compared with the cost of batteries. The more expensive the batteries and the lower the cost of the road grid, the smaller mesh size and vice versa. 

The picture shows a combination of electrifying roads and batteries. It is assumed that batteries cost 350 USD/kWh. This is not the current cost yet but the stated goal for most manufacturers of electric car batteries. 

The cost to electrify the road is assumed to be four million SEK per km, which is the cost assumed for conductive charging (Elways solution).