Ionised Air Battery: Can a Potential Difference Exist?

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P K Pillai
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Radioactive material ionises the air around it.
Carbon nano tubes have an extremely large surface area, & could possibly "store" the ionised charge.
If a volume of carbon nano tubes is wrapped around a core of insulated radioactive material, can a potential difference exist between the wrapping & the core?
 
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Charge effects are challenging to manage, especially within a short radius of a radioactive core.
There have been efforts to harness radioactivity to create electric power directly by using the radiation to excite a phosphor. The emitted light then drives solar cells which produce electric power. The overall efficiency here is not high, but the setup is reasonably safe and robust.