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You can set a static IP on your LAN, but that does not necessarily mean that IP is publicly accessible.
To be maximally helpful for "the network", your node needs to broadcast an IP that anyone can connect.
Most residential Internet service does not include a public IP, rather your router is behind a carrier grade NAT, meaning you cannot forward ports.
Additionally, many Internet plans have data caps that make it "expensive" to sync a node from genesis quickly, let alone seed blocks to others.
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Oh! I wasn't talking about a static ip on a local network but on a public network (aka internet :)).
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If you don't have a static IP but are still able to forward ports using a dynamic IP, then, when your IP changes, all connections will be dropped. Your node will reopen all outgoing connections using your new IP address. Unfortunately incoming connections will not be reopened and any remote nodes will have to wait for your node's new external IP address to be advertised again by your peers.
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I think that paid (@DarthCoin mentioned that) is always static. But I think that if you have public dynamic IP on your router (which is in 99% free) then you can use "discover" parameter in bitcoin core so it will find out that public IP it self and will use it.
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