The initial device fitted to Tony is already implanted within his chest cavity... enter image description here
And the initial accompanying power source (the one the device was designed to draw from) is anything but superficial...
The job performed by Dr Yinsen is effectively surgical triage; a short term fix to keep tony alive. What we see in the first picture is merely the exposed connections, the visible 'tip' of the iceberg. Yinsen had no idea Tony would wake up and develop the arc reactor, and will not have designed the electromagnet with that in mind.
The mini arc reactor Tony creates is another 'rush job' necessitated by circumstance rather than careful planning; albeit truly the mind of a genius is able to improvise such a technology. To be blunt; the original device in his chest was a short term measure, and as such needed a short term power supply.
We can see from the first photo that the flesh around the wound is looking as though it is turning septic. We see Tony remove the power source and replace it later in the movie, with the assistance of Pepper.