Ah I got what you are asking. Umm.. I guess there is no fixed term for it but you may say words like '입력창', or '입력하는 창', or '입력하는 칸' to express it. Especially for the search engine, it would be '검색창'.
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December 26, 2018
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Answered
No 'ch' sound. Usually 'ㅈ' is pronounced as alphabet 'J' in English without so much difference.