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An electric field E = 30x² i (in SI units, with x in metres) exists in a region. Determine the potential difference V0 - VA, where V0 is the potential at the origin and VA is the potential at x = 2 m.

1. -80 V
2. 80 V
3. 120 V
4. -120 V

Correct answer: 80 V

Solution

The potential difference V0 - VA = -(VA - V0) = -[-integral from 0 to 2 of E dx] = integral from 0 to 2 of 30x² dx = 30*(x³/3) from 0 to 2 = 10*(8) = 80. So V0 - VA = 80 V (the units, though written as J, are volts).

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