Electric potential at a point (x, y, z) m in a field is given by V = 5x² volt. Then the electric field at the point (1, 2, 3) m is ⃗E = N C⁻¹.

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Accepted Answer

(4) -10 ̂i. Given: V = 5x² (no y or z dependence); point (1, 2, 3) m. Idea: ⃗E = -((∂ V)/(∂ x)̂i + (∂ V)/(∂ y)̂j + (∂ V)/(∂ z)̂k). (∂ V)/(∂ x) = 10x, while (∂ V)/(∂ y) = (∂ V)/(∂ z) = 0. At x = 1: ⃗E = -10x ̂i = -10 ̂i N C⁻¹. The minus sign means the field points towards decreasing potential. So ⃗E = -10 ̂i N C⁻¹.

Electric potential at a point (x, y, z) m in a field is given by V = 5x² volt. Then the electric field at the point (1, 2, 3) m is ⃗E = ___ N C⁻¹.

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