Why Potential Is Positive for +q and Negative for -q

Physics · Electrostatic Potential And Capacitance · NEET

Electric potential due to a point charge is V = (1/4πε₀)(Q/r) = kQ/r. Since k and r are always positive, the sign of V is simply the sign of Q. So a positive charge (+q) makes V positive everywhere around it, and a negative charge (-q) makes V negative everywhere. Memory hook: "V wears the charge's shirt" — potential carries the same sign as the charge that creates it.
rV = 0 (at infinity)+V = +kQ/r (positive)V = -kQ/r (negative)for +qfor -qV has the SAME sign as the charge Qk > 0 and r > 0, so only Q sets the sign
V vs r for a point charge: a +q makes potential positive (red curve above the V=0 line), a -q makes potential negative (blue curve below it). Only the sign of Q decides, because k and r are always positive.

Your doubts, answered

Why is V positive for +q but negative for -q if the formula is the same?

The formula V = kQ/r stays the same, but you must put the charge in WITH its sign. For +q you get V = k(+q)/r which is positive. For -q you get V = k(-q)/r which is negative. Distance r is always positive and k is a positive constant, so only Q decides the sign. Nothing else in the formula can flip it.

Does potential point in a direction like the electric field?

No. Potential (V) is a scalar. It has only a value and a sign (+ or -), no direction. Electric field (E) is a vector and has a direction. Do not confuse the minus sign of potential (which means 'below zero, like a valley') with a direction. The minus sign of V is just a number sign, not an arrow.

If potential is negative, does that mean the field is also negative?

Not directly linked in sign. Around a lone -q, the potential V is negative everywhere, but the field E points radially inward (toward the charge). Around a lone +q, V is positive and E points radially outward. The sign of V tells you it is below the zero level chosen at infinity; the direction of E is a separate fact. Keep V (scalar sign) and E (vector direction) as two different ideas.

Why do we say potential is zero at infinity?

We choose infinity as the reference (zero) point because as r becomes very large, kQ/r becomes very small and tends to 0. From that zero baseline, moving toward a +q climbs to positive V (like climbing a hill), and moving toward a -q drops to negative V (like going into a valley). This is why +q gives V > 0 and -q gives V < 0.

Does the sign of the test charge change the sign of V?

No. Potential V at a point depends only on the SOURCE charge Q that creates the field, not on any test charge you bring. V is a property of the point in space. The test charge only matters for potential ENERGY U = qV, where q is the test charge. Do not mix V (source-only) with U (uses the test charge).

⚠️ The NEET trap
Potential near a negative charge is positive because 'potential is always positive' or because distance and magnitude are positive.
Potential takes the sign of the source charge. Near -q the potential is negative: V = kQ/r with Q = -q gives V < 0. Only Q carries a sign; k and r are always positive.
🧠 Ask yourself: did I put the charge in WITH its minus sign? If Q is negative, V must come out negative.

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Frequently asked

Is electric potential a scalar or vector?

Electric potential is a scalar quantity. It has a magnitude and a sign (+ or -) but no direction. Electric field is the vector; potential is the scalar.

What is the formula for potential due to a point charge?

V = (1/4πε₀)(Q/r) = kQ/r, where k = 9 × 10^9 N m^2 C^-2, Q is the source charge (with its own sign), and r is the distance from the charge. This is directly from NCERT.

Can electric potential be negative?

Yes. Potential is negative around a negative charge, and can be negative anywhere the net effect of negative charges dominates. Negative V simply means the potential is below the zero level chosen at infinity.

Does potential depend on the test charge?

No. Potential V at a point depends only on the source charges creating the field. The test charge only appears in potential energy, U = qV.

Why is potential zero at infinity?

Infinity is the chosen reference point. As r tends to infinity, kQ/r tends to 0, so V = 0 there. All other potentials are measured relative to this baseline.