Distance or length specification (or limit) of Arduino IO devices
Actually, you should use multiple Arduinos (or microprocessors). One for the sensor, one for the bar led. And if the Arduino controlling the coil is at a different position use an Arduino for that one too.

All these Arduinos need to talk to each other. I assume you don't need much data to transport (or maybe you do, this depends on the frequency the sensor need to be read out).

If you are new to Arduino, split your project in parts:


Control with an Arduino the led graph
Control with an Arduino the sensor
Control with an Arduino the coil
Establish a (wireless) connection between two Arduinos
Implement the connection to all of them.


Anyway, you should find a way to let these Arduinos communicate. Since the distances are far, if you don't like wires, find an RF that might work. There are several frequency bands and transceivers (like nRF24L01 for 2.4 GHz, and others for sub 1 GHz bands). Each have their cons and pros. Note that 100 m is quite a distance, so using only an nRF24L01 without decent antenna might not work.

As seen in the comments (and above), you have to make a decision to use wired or wireless communication.

Pros for wired


More reliable (less interference)
Easier to implement (e.g. CAN, RS485)
You might have to spend tests what RF will work (best) 


Pros for wireless:


No need to lay wires
Easier to change positions (in case cables need to be attached)
Less costly (no cabling)