Mobil Oil Co. further dashed the hopes of those who think there is oil off the East Coast of the United States when the company announced today it has abandoned an exploratory well off the New Jersey shoreline.

It was the second exploratory well Mobil has abandoned in its search for oil and gas off the East Coast, an area that petroleum geologists and the oil companies once thought would produce significant discoveries of crude oil and natural gas to augment the nation's rapidly dwindling reserves.

Mobil said that any future drilling it does in the so-called Baltimore Canyon region offshore "will depend on further analysis of drilling results."

But the company's actions did not indicate it had much faith in the future of drilling in the area. It said it would move the giant drilling rig from the East Coast to the Gulf of Mexico.

Last year, when Mobil announced it was abandoning the first well, it moved the drilling rig 35 miles to the south, to begin drilling on the well it abandoned today.

Mobil is not the only oil company to come up dry in the expensive drilling tracts purchased from the government in 1976. So far, at least 11 wells have been drilled to completion and 10 have come up with no significant amount of oil or gas.

Because of the disappointing lack of success in finding oil off the East Coast, oil companies paid only $41.7 million for exploration rights last February, the second auction of East Coast off-shore tracts the government has held.

In August 1976, when hopes for significant discoveries were high, oil companies paid $1.1 billion for 93 of the 154 tracts put up for sale. In February, oil companies only bothered to bid on 44 of 109 tracts.

Only Taxaco has scored a potential success. Last August it said it had discovered what might be enough natural gas to justify production. But the company cannot be sure until it finds out how big the gas field is - which it is doing by drilling other wells around the one which struck gas.

Texaco has drilled a second well about a mile and a half away from the first one which came up dry. The company is now drilling on an adjoining tract that is owned by a group headed by Tenneco. A Texaco spokesman said drilling began March 1 and the company does not expect it to get deep enough to make a judgment on the extent of the field until mid-summer.

The well that Mobil abandoned today was started Jan. 6 and had reached a depth of 13,992 feet. The company headed a group that paid $3.1 million for the right to drill in the area in question (called Block 17 by the Interior Department).

The other companies with interests in the well are Getty, Sun, Diamond, Shamrock, Amerada Hess and Marathon.

The so-called Baltimore Canyon stretches along a large portion of the East Coast with the most promising areas ranging from New York to Virginia.