Table of Contents
Mistake Buster — How to Use
This page lists the 5 most common mistakes students make in Electric Charges and Fields. For each mistake: read what goes wrong → understand why → memorise the correct approach. Check this page the night before your exam.
Mistakes to Avoid
01
Scalar Addition of Electric Fields
Superposition Principle
✗ What students write
Students simply add the magnitudes of the electric fields from multiple charges directly as algebraic numbers.
$$E_{net} = E_1 + E_2 + E_3$$
⚑ Why this is wrong
Electric field is a vector quantity. It has both magnitude and direction. Adding them as scalars completely ignores the angles and spatial orientation of the field lines, leading to a mathematically incorrect net field.
✓ Correct approach
Always treat electric fields as vectors. Resolve them into $x$ and $y$ components or use the parallelogram law of vector addition to find the resultant field magnitude and direction.
$$|\vec{E}_{net}| = \sqrt{E_1^2 + E_2^2 + 2E_1E_2\cos\theta}$$
Remember it as: Fields are arrows, not just numbers. Add them tail-to-tip!
02
Ignoring the “Enclosed” in Gauss’s Law
Electric Flux & Gauss’s Theorem
✗ What students write
Taking the total charge present anywhere in the vicinity of the surface to calculate the net electric flux.
$$\Phi = \frac{q_{total}}{\epsilon_0}$$
⚑ Why this is wrong
Gauss’s Law strictly states that the net flux through a closed surface depends only on the charge enclosed by that specific surface. Charges located outside the Gaussian surface contribute zero net flux because their field lines enter and leave the surface.
✓ Correct approach
Clearly identify the boundaries of the Gaussian surface. Find the algebraic sum of only the charges physically inside it, and use that as $q_{enclosed}$.
$$\Phi = \oint \vec{E} \cdot d\vec{A} = \frac{q_{enclosed}}{\epsilon_0}$$
Remember it as: If it’s not inside the box, it doesn’t count for the flux!
03
Forgetting the Dielectric Constant
Coulomb’s Law in a Medium
✗ What students write
Using the standard permittivity of free space ($\epsilon_0$) to calculate electrostatic force, even when the question specifies the charges are placed in a medium like water or oil.
$$F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \text{ (when in a medium)}$$
⚑ Why this is wrong
The force between charges decreases when they are placed in a dielectric medium because the medium gets polarized and creates an opposing electric field. $\epsilon_0$ is only valid for vacuum or air.
✓ Correct approach
You must multiply $\epsilon_0$ by the relative permittivity or dielectric constant ($K$ or $\epsilon_r$) of the medium, effectively dividing the vacuum force by $K$.
$$F_{medium} = \frac{1}{4\pi\epsilon_0 K} \frac{q_1 q_2}{r^2} = \frac{F_{vacuum}}{K}$$
Remember it as: Medium matters! Divide the free-space force by $K$.
04
Flipping Dipole Field Directions
Electric Field due to an Electric Dipole
✗ What students write
Assuming the electric field on the equatorial line points in the same direction as the dipole moment vector ($\vec{p}$).
$$\vec{E}_{equatorial} \text{ is parallel to } \vec{p}$$
⚑ Why this is wrong
The dipole moment $\vec{p}$ is directed from $-q$ to $+q$. However, on the equatorial plane, the net electric field resolves horizontally pointing from $+q$ towards $-q$ (opposite to the dipole moment).
✓ Correct approach
The electric field on the axial line is along $\vec{p}$, but on the equatorial line, it is purely anti-parallel to $\vec{p}$. Notice the minus sign in the vector form formula.
$$\vec{E}_{axial} \parallel \vec{p} \quad \text{and} \quad \vec{E}_{equatorial} \parallel -\vec{p}$$
Remember it as: Axial Agrees, Equatorial Opposes (the dipole moment).
05
Misplacing the Null Point for Unlike Charges
Equilibrium of Charges
✗ What students write
Searching for a neutral point (where the net electric field is zero) somewhere between two opposite charges.
⚑ Why this is wrong
Between two opposite charges (one positive, one negative), the electric fields from both charges point in the same direction. Since they point the same way, they add up and can never cancel each other out.
✓ Correct approach
The null point for two unlike charges always lies outside the line joining them, positioned on the side of the charge with the smaller magnitude.
Remember it as: Opposites repel the null point outside! (Always near the weaker charge).
Pre-Exam Checklist
Electric Charges and Fields — Mistake Checklist
Go through this 5 minutes before your exam
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Check if you added electric fields as vectors (using angles) or incorrectly as scalars.
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Confirm only enclosed charges are used when applying Gauss’s Law.
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Verify if charges are in a medium and include the dielectric constant ($K$) if necessary.
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Ensure $\vec{E}$ on an equatorial plane is drawn opposite to the dipole moment $\vec{p}$.
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Place the null point outside the line joining two unlike charges, near the smaller charge.
