Superposition Principle: Force Between Multiple Charges

Physics · Electric Charges And Fields · NEET

The superposition principle says the net force on one charge is just the vector sum of the separate Coulomb forces from every other charge, and each of those forces is unchanged by the presence of the others. So you calculate each pair force with F = k·q1·q2/r^2, then add them as vectors: F_net = F1 + F2 + F3 + ... Memory hook: "each pair minds its own business, then you add the arrows."
Net force on q1 = vector sum of F12 and F13q1q2q3F12F13F_net = F12 + F13
Each other charge exerts its own Coulomb force on q1 (F12 from q2, F13 from q3). These are added as vectors to give the net force F_net; neither pair force is changed by the presence of the third charge.

Your doubts, answered

Do the other charges change the force between two given charges?

No. This is the key idea of superposition. The force on q1 due to q2 is exactly the Coulomb force k·q1·q2/r12^2, whether or not q3, q4, ... are present. Nearby charges do NOT weaken or strengthen a pair force. They only add their OWN separate forces on q1. NCERT states this clearly: the force on q1 due to q2 is unaffected by the presence of other charges.

Why do I add the forces as vectors and not just add the numbers?

Because force has direction. F1 from a charge on the left and F2 from a charge above point in different directions. Adding numbers only works if the forces are along the same line. For charges at angles you must break each force into x and y components, add components, then combine: F_net = sqrt(Fx^2 + Fy^2). For NEET, always draw the arrows first.

Is the superposition principle the same as the law of vector addition?

Not exactly, and NEET can test this. Vector addition is only the second half. Superposition says TWO things: (1) each pair force is unaffected by other charges, and (2) there are no extra three-body or four-body forces that appear only when many charges are present. Once you accept (1) and (2), you then use ordinary vector addition to get the total.

How do I find the net force on a charge placed at the centre or corner of a shape?

Find the force from each other charge separately using F = k·q·q'/r^2, mark its direction (attraction points toward the other charge, repulsion points away). Then resolve into components and add. Symmetry is your shortcut: equal charges placed symmetrically often give forces that cancel, leaving a simple net direction. At the centre of a square with 4 equal like charges, the net force is zero by symmetry.

If a charge is exactly midway between two equal charges, what is the net force on it?

If the two outer charges are equal and like-signed, they push (or pull) the middle charge with equal and opposite forces, so the net force is zero. But note: this is an unstable equilibrium along the line and the field there can still be non-zero for a test charge off-axis. Superposition gives zero net force here purely because the two equal forces cancel.

⚠️ The NEET trap
Adding the magnitudes of all Coulomb forces directly to get the net force.
Add the forces as VECTORS. Resolve into x and y components, add components, then take F_net = sqrt(Fx^2 + Fy^2). Magnitudes only add directly when all forces lie on the same straight line.
🧠 Forces are arrows, not just numbers. Draw them before you add them.

Real NEET questions

NEET 2019

Two point charges A and B, having charges +Q and -Q respectively, are placed a certain distance apart and the force acting between them is F. If 25% of the charge of A is transferred to B, then the force between the charges becomes

A · F
B · 9F/16
C · 16F/9
D · 4F/3
Solution: Original force: F = k·Q·Q/d^2 = kQ^2/d^2. Transfer 25% of A's charge (0.25Q) to B. New charge on A = Q - 0.25Q = 0.75Q. New charge on B = -Q + 0.25Q = -0.75Q. New force magnitude F' = k·(0.75Q)(0.75Q)/d^2 = k·0.5625Q^2/d^2 = (9/16)·kQ^2/d^2 = (9/16)F. Answer: 9F/16.
NEET 2025

Two identical charged conducting spheres A and B are separated by a distance, each carrying charge q, with force of repulsion F between them. A third identical uncharged sphere is touched to A first, then to B, and finally removed. The new force of repulsion between A and B is

A · F/2
B · 3F/8
C · 3F/5
D · 2F/3
Solution: Start: A = q, B = q, F = kq^2/d^2. Uncharged sphere C touches A: identical spheres share equally, so A = q/2, C = q/2. Then C (q/2) touches B (q): total (q/2 + q) = 3q/2 shared equally, each = 3q/4, so B = 3q/4. Final: A = q/2, B = 3q/4. New force F' = k·(q/2)(3q/4)/d^2 = (3/8)·kq^2/d^2 = 3F/8.

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Frequently asked

What is the superposition principle in electrostatics?

It states that the total electric force on a charge is the vector sum of the individual Coulomb forces due to each of the other charges, and each pair force is independent of the other charges present.

What is the formula for net force by superposition?

F_net = F1 + F2 + F3 + ... (added as vectors), where each Fi = k·q1·qi/ri^2 points along the line joining the pair, with k = 1/(4·pi·epsilon0) = 9 x 10^9 N·m^2/C^2.

Does superposition work for electric field too?

Yes. The net electric field at a point is the vector sum of the fields due to each charge: E_net = E1 + E2 + ... The same principle applies to force, field, and potential.

When does the net force become zero by superposition?

When the vector sum of all individual Coulomb forces cancels. This often happens due to symmetry, for example at the centre of a square with four equal like charges, or midway between two equal like charges.

Is superposition valid only in vacuum?

The principle itself holds in any medium. In a uniform medium you replace k by k/K (K = dielectric constant), but each pair force is still computed independently and then added as vectors.