Question

the electric potential in a certain region of space is given by v = -7.5x² + 3x, where v is in volts and x is in meters. in this region the equipotential surfaces are
○ concentric spheres centered at the origin.
○ concentric cylinders with the x - axis as the cylinder axis.
○ planes parallel to the x axis.
○ planes parallel to the yz plane.
○ unknown unless the charge is given.
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Explanation:

Step1: Recall the relationship between electric - potential and equipotential surfaces

Equipotential surfaces are surfaces where the electric potential \(V\) is constant. Given \(V=-7.5x^{2}+3x\), since \(V\) is a function of \(x\) only, the surfaces of constant \(V\) will be planes perpendicular to the \(x\) - axis, or in other words, parallel to the \(yz\) - plane.

Answer:

planes parallel to the yz plane.