Can I use it to obtain an e-visa to enter Turkey on 10th Aug? my Schengen visa will expired on 14th June
No. According to http://www.mfa.gov.tr/visa-information-for-foreigners.en.mfa Egyptian passport holders are required to have visa to enter Turkey.
A valid Schengen visa or residence permit and travel to Turkey with Turkish Airlines or Egypt Air is required to obtain a 30-day single-entry e-Visa.