Understanding how V+ and V- combine to give the total potential in electric fields.

What happens when you stand at a point in space and ask, “What’s the total potential here?” It’s a little like standing on a hill made up of several smaller hills. Each hill has its own height, and when you stack them together, you get the total landscape you feel under your feet. In physics terms: the total electric potential at a point is the sum of the potentials contributed by each charge or source. And in the language of the problem you shared, that means Vtotal is the sum of Vplus and Vminus.

Let me unpack that a bit so it clicks, not just sticks as a formula you memorize.

What is electric potential, really?

Electric potential, V, is the energy per unit charge at a point in an electric field. It’s a scalar quantity, which means it has magnitude but no direction. That’s handy, because when we’re adding things up—potential contributions from different charges—we’re summing scalars, not vectors. Simple addition, without worrying about directions getting tangled.

Why Vplus and Vminus?

When you set up a scene with multiple charges, each charge creates its own potential field. If you have a positive source, it contributes a positive amount to the potential at your point; a negative source contributes a negative amount. If you label the contributions as Vplus (from the positive sources) and Vminus (from the negative sources), then the total potential at your point is

Vtotal = Vplus + Vminus.

That’s the essence of superposition for potentials: you just add the individual contributions, no fancy tricks required. It’s a clean, scalar superposition, unlike the electric field, which is a vector and also adds, but with directions to respect.

A tiny math detour, kept simple

For a point charge qi located at ri, the potential at a point P a distance riP away is

Vi = k * qi / |rP − ri|,

where k is Coulomb’s constant (about 9 × 10^9 N·m^2/C^2). If you have several charges, you compute each Vi and then sum:

Vtotal(P) = Σ Vi = Σ k * qi / |rP − ri|.

If you want to separate the contributions into Vplus and Vminus, you’d group all the terms from positive charges into Vplus and all the terms from negative charges into Vminus, then add them:

Vplus = Σ (k * qi / distance for all positive qi),

Vminus = Σ (k * qi / distance for all negative qi),

Vtotal = Vplus + Vminus.

Two-charge intuition

Let’s ground it with a concrete two-charge scenario. Suppose you have:

• a positive charge q1 = +1 μC at some location,

• a negative charge q2 = −1 μC at another location.

From a given point P, the distance to each charge is r1 and r2, respectively. Then

V1 = k * (+1 μC) / r1,

V2 = k * (−1 μC) / r2.

Add them:

Vtotal = V1 + V2.

If r1 and r2 are the same, the magnitudes cancel and Vtotal could approach zero (depending on the exact distances). If one distance is much smaller than the other, you’ll feel the closer charge more strongly in the potential. The sign of Vtotal tells you whether the point sits in a region dominated by positive or negative influence, but you always get a single scalar value for Vtotal.

Why this matters for NEET-level thinking

In the NEET physics world, you’ll encounter problems that ask you to compare potentials from multiple sources, or to compute the total potential at various locations. The neat thing is: because potential is scalar, you don’t need to keep track of directions while adding. You simply add the numbers. It’s a different vibe from electric fields, where vectors care about directions and components.

A quick practical approach you can use on problems

• Identify all sources contributing to the potential at the point of interest.

• Determine whether each source is positive or negative in charge, so you know the sign of its contribution.

• For each source, compute Vi = k qi / ri (the distance is the straight-line distance from the source to the point in question).

• Sum all Vi to get Vtotal. If you’ve separated the contributions, sum Vplus and Vminus to get Vtotal.

A tiny example you can picture

Imagine you’re at point P, with two charges:

• q1 = +2 μC at a distance r1 = 1 m,

• q2 = −1 μC at a distance r2 = 0.5 m.

Compute each contribution:

• V1 = k * 2e-6 / 1 = 2k × 10^-6 ≈ 18,000 V,

• V2 = k * (−1e-6) / 0.5 = −2k × 10^-6 ≈ −18,000 V.

Add them, and in this tidy setup, Vtotal ≈ 0. The closer negative charge pulls the potential down more strongly, canceling the positive contribution from the farther positive charge. Real life isn’t always so tidy, but the principle stays: add the pieces and you see the whole picture.

A few subtle but helpful contrasts

• Potential vs. field: Potential is a scalar; electric field is a vector. Both superpose, but you add scalars in the potential case and vectors in the field case. This often makes potential problems feel a touch easier at first glance.

• Zero reference: We often set the reference potential to zero at infinity. That choice doesn’t change the physics; it just gives you a clean baseline to work from.

• Signs matter: A negative source lowers the potential at a point; a positive source raises it. When you sum, watch those signs; a careless sign slip is a notorious little gremlin in problem-solving.

Relatable takeaways

• The phrase “Vplus and Vminus” isn’t about two separate physical things floating in space; it’s a bookkeeping method. You’re tallying how much potential each group of sources contributes and then combining them.

• The idea mirrors everyday intuition: if you stand in a room with multiple voices, the room’s mood (the total “potential” vibe) is the sum of each voice’s contribution. Some voices lift you up (positive potentials), some pull you down (negative potentials). The net vibe is the total potential.

A gentle nudge toward deeper understanding

If you’re curious about real-world analogies, try thinking about gravitational potential as a parallel. Masses create a gravitational potential field, and the total gravitational potential at a point is the sum of each mass’s contribution. The math looks similar, though the constants and units shift to gravity’s language. It’s surprising how often these “same math, different physics” moments help solidify understanding.

Putting it all together

So, when the question asks which variables are summed to get the total potential, the answer is Vplus and Vminus. It’s a clean, scalar superposition: add the contributions from positive sources and from negative sources, and you get the complete picture at any point in space.

If you’re exploring this topic further, a few problems that feel like little puzzles can reinforce the idea:

• A point P near two charges where Vplus and Vminus nearly cancel. What does Vtotal look like?

• Two positive charges at different distances from P. How does their combined Vtotal compare to each individual Vi?

• A mix of several charges with varying distances. Can you predict the sign of Vtotal just by looking at the closest charges?

In the end, the beauty of total potential lies in its simplicity. It’s one of those ideas that appears deceptively straightforward—yet it gently unlocks a lot of the behavior you’ll see in electrostatics. And once you’ve got the hang of summing Vplus and Vminus, you’ve built a solid stepping stone toward tackling a broader swath of NEET physics topics with confidence.

If you want, we can walk through more examples or tighten the intuition with a few guided problems. Think of it as a calm, clear walk through a tiny landscape of hills—you’ll see how every little peak contributes and how the final view comes together.