If you have two solar panels do you have to have two separate controlers for two separate batteries?

No, the solar panels cane wired in parallel, and use one charge controller to drive a battery.

can 10wat solar power a laptop

No, a first step to figure if it will power something is read the power supply of your computer of device. Chances are great the computer power supply reads that it consumes more than 65 watts and perhaps up to 100watts (read the "rated at xx watts") . Next step is realize this power rating for solar is over rated and only available at high noon and with zero cloud cover, so it must charge for quite a while to charge a battery to run your laptop. So you really want about a 200W solar panel to power a 100W laptop, assuming you have a battery to store the charge and run the laptop when the sun is not at optimum. Also the laptop is rated at 19v-21v so you need a booster/inverter to either go from 12V to 19V (95% energy efficient) or a 12V to 110V and use your 110v adapter to 19v (80% energy efficient).

Will this keep a 12v car or deep-cycle battery charged? Trying to install IP camera remotely with solar & battery setup

A 10 Watt panel with 6 hours of good sun per day will only provide you 60 watts of energy. At 12Volts that's a replacement power of 5 amps per day. So, if your camera is going to consume more that 5 Amps per day then no it won't work for you. You will also need a charge controller of some sort as well.If you were going to use this as a trickle charger for a battery that doesn't get used every day then maybe it would work for you. But if this is a 24 hours a day operation then I would op for a bigger panel.

Brand	ECO-WORTHY
Material	Monocrystalline Silicon
Product Dimensions	13.3"L x 8.1"W x 0.7"H
Item Weight	0.76 Kilograms
Efficiency	High Efficiency
Included Components	Solar Panel module
AC Adapter Current	0.56 Amps
Maximum Voltage	12 Volts
Maximum Power	10 Watts
Manufacturer	ECO-WORTHY
Part Number	AM-P10-N-1
Item Weight	1.67 pounds
Item model number	AM-P10-N-1
Is Discontinued By Manufacturer	No
Size	10W
Color	blue-black
Style	Battery
Power Source	Battery Powered
Wattage	10 watts
Item Package Quantity	1
Cutting Diameter	13.3 Inches
Special Features	Lightweight,Waterproof
Batteries Included?	No
Batteries Required?	No
Assembled Diameter	13.3 Inches

10 Watts Solar Panel

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