Is potential energy and "work done" the same thing?

If they are not one and the same thing then why is potential energy always associated with "work done"?

Could you explain me with some examples?


Question: Is it possible to extend the reach of a pn532 NFC/RFID shield?
Answer: Adafruit's PN532 board has been meticulously designed in order to get the maximum range out of it: PN532 - Breakout Board. That being said it is possible to increase the range by using a powered(active) tag instead of an unpowered (passive) tag. 

For your problem it sounds like it needs to remain passive, but so long as you get the antenna to be as close to the top of the shoebox as possible and are using of the larger ones like Adafruit's reader and there is NO METAL ANYWHERE near the reader it should be enough to read most tags from a reasonable distance.

So why can't you increase the range for a passive tag?

The electromagnetic field between the two which is used to communicate information falls off rather dramatically as you get further from the source, which makes it increasingly difficult to power the tag. 

So without going into deep physics, in order to increase the range of the PN532 board you need to either increase the diameter of the coil, which increases the size of the electromagnetic field, and/or increase the power output through the coil.

The approximate equation for the area of the radius in respect to the desired read range is:

$$ a = \sqrt{2r}$$

Where \$a\$ is the area of the coil and \$r\$ is the read distance from the coil.

But this causes issues as well, in order to increase the diameter of the coil you need to increase the length of the trace which increases the total resistance of the system and decreasing the effectiveness of the coil. 

That ignored modifying the antennae changes the inductance of the antennae, the row of capacitors leading to the antennae is a frequency and impedance matching circuit, changing the antenna means that you need to modify all of those components in order to get it work.

Or we could supply more power, except the PN532 has an upper limit on the amount of power it can push through the antenna, which makes this unreasonable. So you would have to build your own RFID reader.

The simplest ever designed is here, it is designed for 125khz not 13.56mhz but in theory you can push however much information you want through this coil and it will continue to function(granted you would have to protect whatever is reading the coil...)