Answer by Mark Adler:
A Tesla gets about 3 miles per kWh. Let's say on average the speed is 45 mph. So the power draw is about 15 kW. (Pretty efficient! That's only about 20 hp.)
Let's cover the roof and hood with solar panels. I get maybe 4 square meters. The maximum insolation at noon at the equator (we'll assume that you live in Ecuador) on that would be about 4 kW. We'll use higher efficiency panels at 15%. So we're at 600 W. At the equator. At noon. We're getting maybe 4% of the car's energy usage. Once reality is factored in, you'll be lucky to get 2%. More like 300 W.
So charging "on the go" might extend your range by 2%. Hardly worth it since those panels will cost a lot. The 300 W worth of panels will charge up the 60 kWh battery (the smaller one they used to sell) in about 200 hours of decent daylight. Close to a month! So you can't even expect a detectable charge boost while you were in the grocery store.
Even if solar cell efficiencies were up around 30% or 40% efficiency at a reasonable cost (right now those are a few hundred times the cost of 15% cells, used for things like spacecraft), the results only change by a factor of two or so. Solar cells on a car can't work out unless the car is incredibly small, light, and aerodynamic. There are competitions for solar powered cars like that. This is what they look like (not like a Tesla), weigh less than 300 kg, and use super-expensive triple-junction solar cells:
So, bad idea for a production car. Better to put solar panels on the roof of your house, store that energy in your power company during the day, and get it back from the power company at night to charge your car. Not only is your roof way bigger than your car, but you can also get cheaper panels, since depending on your roof size, they don't need to be very efficient.
If you look deep in the comments below, you will see an example provided by Vikrant Vaidya which begins to show benefits for a car solar panel on this a very efficient electric vehicle, the Mahindra E2O EV:
That car is more than twice as efficient in km/kWh than a BMW i3, and with a 1.5 m^2 solar panel, you can get around 7.5% of a full charge per day. Depending on how close your daily use is to the capacity of the battery, the solar panel could make the difference.