I know that Nazi Germany was severely lacking in oil reserves, which is a major reason for the invasion of the USSR. There's a lot of coal in Germany; why not make their Panzers run on electricity generated via coal power? The Battle of the Bulge and Kursk would have gone much better for the Germans if their tanks weren't worried about running out of gas.
Without wishing to sound too snarky, this is a little like asking why Napoleon didn't use the train to invade Russia when all of his horses kept dying in 1812.
It certainly is the case that electric vehicles have actually been around since the late 19th Century, and up until roughly the First World War were actually quite popular, particularly in America. This is because rapid electrification and urbanisation allowed for their effective use as town cars, where drawbacks such as their low range and speed didn't matter, but the ability to cheaply recharge them was useful. For long-distance travel however, things were not so rosy for the electric car. As until very recently, the main drawbacks of electric vehicles came from, essentially, their inefficiency. That is to say that compared to a similar internal combustion engine, a battery powered engine could not sustain a substantial enough charge to provide for speeds over about 18-20mph or for long distances. This issue was further compounded by advancements in the 1910s and 1920s such as mass production, oil exploration and mass infrastructure projects which not only made the internal combustion engine far cheaper than electric vehicles, but also overwhelmingly more practical.
To focus a little more specifically on military vehicles, tanks in particular are already infamous for their vast fuel costs. The War Office Miltary Vehicles and Engineering Establishment recorded in WW2 that the M4 Sherman supplied to the British army managed approximately 1.2 mpg, which dropped to ~0.5 mpg on rougher terrain. This figure was even lower on later, more heavily armoured models (WO 194 in the National Archives). With a 180ga tank, his would give the Sherman an effective operational range of approximately 90-180 miles depending on terrain. Allied logistics were such that the 'echelon' squadrons of armoured regiments were often able to keep relative pace with the operational squadrons with fuel tankers, and extend this range.
In the heavier German tanks like the Tiger, fuel efficiency was far worse. The Tiger averaged about 0.3 mpg, meaning that its effective operational range was only around 65 miles cross-country. Other German tanks such as the Panther were infamous for their poor engine power, with post-War British engineers noting that the Panther in particular was extremely prone to spontaneous combustion as its woefully underpowered gearbox failed to cope with the excessive armour weight of the vehicle. In this context, an electrical engine is incredibly impractical. Even if design had been maintained during the 1920s, the engines of the time would have left German tanks, or really any tanks, with woeful top speeds and incredibly short operational ranges compared to their conventially-powered contemporaries, as well as being exponentially more expensive before we even come to the various precious metals that would be needed to mass-produce the batteries sufficient to power an armoured force.
I'm also slightly confused as to how the logistics of such a situation would be possible. As mentioned previously, electric cars became popular in the early 1900s in urban environments because they could be readily recharged. Battlefields, particularly those on the Russian steppe, are not widely known for their readily available supplies of electricity, and short of designing a giant, mobile power station or a fleet of giant capacitor vehicles, refuelling in the field would be extremely impractical. Given the manufacturing shortcomings already faced by the Germans, it would have not have been practical to forgo tried and tested technology to pour investment into theoretical electric vehicles.
The disadvantage of coal powered electric plants is that they need to be very large. It would not be possible to create a compact coal generator to power a vehicle. For example, the Fort Wainwright power plant generated only 2.5 MW when it went online in 1945. This is about 3300 hp, enough to power about 3-4 heavy tanks, given 100% efficiency in converting electrical energy to mechanical. In reality, the efficiency would be significantly less than that. Seeing as how locomotive manufacturers were fleeing traditional coal powered locomotives in favour of diesel electric in the 1940s and 50s, it is quite reasonable to say that this technology could not be miniaturized effectively to power something like a tank.
Another way to supply power would be through batteries, either shipped from Germany or charged locally. If you look at the modern progress of electric cars, power capacity, even with modern battery technology, is still a big issue. Until recently, even electric cars had backup gasoline or diesel engines to run the car when the battery went flat, and this is for a consumer vehicle that would be able to recharge every day (or even multiple times per day), a luxury not available to military vehicles. Another issue with lead-acid batteries, the only type available at the time, was that they had to be charged up every 14-16 hours to avoid sulfation, which reduces battery life. This effect is only accelerated by cold temperatures and over-draining the battery past a certain point. Given the rather flaky situation with German supply lines, it does not seem likely that either a timely exchange of batteries or a widespread network of charging stations could be established.
Finally, assuming we get past all the engineering business of actually getting the electric energy to the tanks somehow, there is still the issue of converting it from electrical to mechanical energy. The Ferdinand used electric generators for power, so experience with it can give us a good indication of what is required for an electric-powered tank. 2 tons of copper was required to make the electric motors for a single Ferdinand. Copper was among many materials that was in short supply in Germany starting with 1942. It would not be possible to make a large amount of tanks powered this way.
As you can see, removing gasoline from the equation introduces a large number of issues that 1940s era technology just couldn't begin to tackle even in optimal conditions, let alone in the situation Germany found itself in.
Sources:
https://www.sourcewatch.org/index.php/Fort_Wainwright_Power_Plant
http://batteryuniversity.com/learn/article/sulfation_and_how_to_prevent_it