If I search something on my iPhone will my service provider know what I searched?

Title says it all.

Yes.

I was wondering that myself

Yes but in certain countries it is against the law so they aren't allowed to keep that information for longer then a few weeks for legal purposes. But since when does the law mean anything for the rich.

The data that they keep isn't publicly available and can only be retrieved via a warrant if you get caught. Sights that you don't want to be caught on usually have IP tracking on them so even if you destroy the evidence on your end that have enough on there's.

In other words don't look up anything you might get in trouble for.

If you access the search engine over plain HTTP, then your service provider can intercept the request and see what you are searching for without any trouble.

If you access the search engine over HTTPS, then they shouldn't be able to… But it has been known for ISPs and Browser vendors to perform man in the middle attacks ( http://www.techweekeurope.co.uk/news/nokia-decrypting-traffic-man-in-the-middle-attacks-103799 ) which would make searches visible to them.

If you want to protect your data from your mobile broadband supplier, you can use a virtual private network: https://www.riseup.net/en/how-vpn-works