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The electric potential at any point (x, y, z) in a region is given by V = 3*x² volt (x in metres). Find the electric field at the point (1, 0, 3) m.

1. 3 V/m, directed along the positive x-axis
2. 3 V/m, directed along the negative x-axis
3. 6 V/m, directed along the positive x-axis
4. 6 V/m, directed along the negative x-axis

Correct answer: 6 V/m, directed along the negative x-axis

Solution

Since V = 3*x² depends only on x, the field has only an x-component: Ex = -dV/dx = -6x. At x = 1 m, Ex = -6 V/m. The negative sign means the field points along the negative x-axis, with magnitude 6 V/m.

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