Don't know that 35,000 feet is up high enough for an effective EMP blast. Most of the tests in the mid-60s were at altitudes between 30 and 60 miles up... I would think that some sort of ballistic missile would be more effective.
There's no doubt that a High Altitude EMP would be most effective, but a detonation at only 40,000 feet could devastate an area several hundred miles wide. A radius of 120 miles from Philadelphia includes Washington, Baltimore and New York City. If successfully detonated, that's enough to bring the USA to a grinding halt.