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The electric potential V at any point (x, y, z), in all meters in space is given by V = 4x² volt. The electric field at the point (1, 0, 2) in volt/meter is

1. 8 along positive X-axis
2. 16 along negative X-axis
3. 16 along positive X-axis
4. 8 along negative X-axis

Correct answer: 8 along negative X-axis

Solution

The electric field is the negative gradient of the potential. Differentiating V = 4x² with respect to x gives E_x = -dV/dx = -8x. At (1, 0, 2), x = 1, so E_x = -8(1) = -8 V/m, which is along the negative X-axis.

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