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title: "Two equal and opposite point charges, \\(+Q\\) at \\(x = -a\\) and \\(-Q\\) at \\(x = +a\\), establish an electrostatic configuration where the electric potential is defined to be zero at infinity. At the origin \\((x = 0)\\), the net electric potential is \\(V = 0\\text{ V}\\), but the electric field is nonzero and points in the \\(+x\\)-direction. Which of the following statements correctly explains how a point with zero electric potential can have a nonzero electric field?"
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url: "https://nerd-notes.com/ubq/121107/"
date_modified: "2026-08-23T04:58:01+00:00"
---

# Two equal and opposite point charges, \(+Q\) at \(x = -a\) and \(-Q\) at \(x = +a\), establish an electrostatic configuration where the electric potential is defined to be zero at infinity. At the origin \((x = 0)\), the net electric potential is \(V = 0\text{ V}\), but the electric field is nonzero and points in the \(+x\)-direction. Which of the following statements correctly explains how a point with zero electric potential can have a nonzero electric field?

Two equal and opposite point charges, \(+Q\) at \(x = -a\) and \(-Q\) at \(x = +a\), establish an electrostatic configuration where the electric potential is defined to be zero at infinity. At the origin \((x = 0)\), the net electric potential is \(V = 0\text{ V}\), but the electric field is nonzero and points in the \(+x\)-direction. Which of the following statements correctly explains how a point with zero electric potential can have a nonzero electric field?

![A horizontal line represents the x-axis with a central tick mark labeled 0. A positive point charge labeled +Q is positioned on the axis to the left of the origin at a tick labeled -a. A negative point charge labeled -Q is positioned on the axis to the right of the origin at a tick labeled +a. An open circle sits at the origin on the axis. A single horizontal arrow points rightward from the origin, labeled \vec{E}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461081-j8cC8K.jpg)

- **A.** The zero electric potential arises because no net work is done moving a test charge from infinity along the equipotential y-axis, meaning the electric field at the origin remains nonzero because the electric field represents the work done per unit displacement specifically along the direction of charge separation.
- **B.** The electric potential is the scalar sum of the individual potentials and equals zero at the origin, whereas the electric field is the negative spatial gradient of the potential, which is nonzero because the potential varies continuously from positive values for \(x < 0\) to negative values for \(x > 0\).
- **C.** The electric potential at the origin is zero because the opposing electric fields of the two charges perform equal and opposite work on any moving charge, which causes the net electrostatic potential energy to vanish while leaving the instantaneous electrostatic force nonzero.
- **D.** The electric potential at a point reflects only the magnitude of the surrounding charge distribution, whereas the electric field depends on the vector sum of the charges, allowing the potential to cancel due to symmetric charge placement while the vector field remains nonzero.

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