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MIHOKO HAKATA, a freelance illustrator and recent art-school graduate, ducked into a coffee shop in Midtown Manhattan last week, desperate for a jolt of energy.

She had work to do. But as she removed her materials from her backpack, it became clear that the energy she was seeking could not be found in a cup. She had a more pressing need: to find a power outlet for her laptop computer, whose battery had died.

“I realized they have this,” said Ms. Hakata, a 29-year-old Tokyo native, as her hand slipped beneath a table to deftly plug her I.B.M. ThinkPad into a wall socket.

Before Ms. Hakata, who lives on a drafty boat on the Hudson River, could settle into her work, a young man clutching a dying cellphone rushed in.

“I just have to charge it,” he said, asking Ms. Hakata if he could share one of the two power outlets under her table. She smiled politely and nodded.

Every day, millions of people are finding themselves scurrying about in search of wells of electricity they can tap so their battery-powered mobile devices can remain mobile. Dependence is growing on laptops, cellular telephones, digital music players, digital cameras, camcorders, personal organizers, portable DVD players and the latest hand-held gaming devices - most of which operate on rechargeable lithium-ion batteries - and finding available electrical outlets away from home and office has become more urgent.