Electric potential can be zero at a point where the electric field is non-zero. At the midpoint of equal and opposite point charges, the two potentials cancel. The two electric fields point from the positive charge towards the negative charge, so their magnitudes add.
For 2027 A-Level H2 Physics 9478, this example connects the formula for point-charge potential with the direction of the electric field. Start each calculation by deciding whether you are adding signed scalar quantities or vectors.
- Use V = kQ/r and keep the sign of the source charge.
- Find each field’s direction using a positive test charge.
- Use the change in potential with position to interpret the field.
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Draw the two contributions
Put +Q on the left, −Q on the right and midpoint M between them. Both sources are the same distance from M. Taking the potential at infinity as zero, +Q gives positive potential and −Q gives negative potential at M. Their magnitudes match.
To find the directions of the fields, imagine a small positive test charge at M. The positive source repels it to the right. The negative source attracts it to the right. Both contributions to the electric field at M therefore point to the right.
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Worked example | Calculate V and E at the midpoint
In air, take the two charges to be +2.0 nC and −2.0 nC, separated by 0.20 m. The distance from M to each source is 0.10 m. Use k = 9.0 × 109 N m² C−2.
At M, each potential has magnitude k|Q|/r = (9.0 × 109)(2.0 × 10−9)/0.10 = 180 V. The contributions are +180 V and −180 V, giving V = 0 V.
Each field has magnitude k|Q|/r² = 1.8 × 103 N C−1. Both point towards the negative charge along the line of the charges. The total electric field is 3.6 × 103 N C−1 towards the negative charge.
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Use the potential gradient as a check
Along the line between the charges, a point slightly left of M is closer to +Q and has positive potential. A point slightly right of M is closer to −Q and has negative potential. Potential decreases as you move to the right through M, so Ex = −dV/dx gives a field to the right.
For practice, replace the negative charge with another +2.0 nC charge at the same position. Both potentials are now positive, so V at M is 360 V. The fields at M point in opposite directions and have equal magnitudes, giving E = 0. Sketch the arrows again when changing a sign.
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Frequently asked questions
Which way would an electron initially accelerate at M in the first example?
To the left, because its charge is negative and the electric force qE points opposite to the field. The field itself still points to the right.
Can two nearby points both have zero potential?
Yes. The perpendicular bisector of equal and opposite point charges consists of points at equal distances from the two charges. Each point has zero potential under the chosen reference. The potential can still change in a direction perpendicular to that bisector.
Is V = 0 enough information to infer the field?
You need information about how V changes nearby. A single potential value gives the height on a potential graph. The field depends on the slope.
Contents · Official syllabus and next practice
Official syllabus and next practice
Read the official SEAB 2027 syllabus
For another worked comparison, read how voltage, current and power change in series and parallel circuits.