Q.21 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 21 Solution

Topic: Electrostatic Potential and Capacitance · Official NTA Booklet Code M1

Question

A parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is: (ε₀ = permittivity of free space)

✓

Verified Against NTA Final Answer Key

Option (3) : 1/2 ε0 E^2 A d

📚 Electrostatic Potential and Capacitance Easy

📋 Given Parameters & Problem Setup

Electric Field Uniform electric field E between plates

Plate Separation d

Plate Area A

Permittivity ε_0

⚡

The 30-Second Exam Hall Shortcut: ⚡ Energy = Energy Density × Volume

⏱️ Save ~20 seconds

Energy density of electric field $E$ in free space is $u = \frac{1}{2}\varepsilon_0 E^2$ . The volume between capacitor plates is $\text{Volume} = A \cdot d$ . Total stored energy is $U = u \times \text{Volume} = \frac{1}{2}\varepsilon_0 E^2 A d$ ! Instant 5-second answer matching Option (3)!

1 Recall electrostatic energy density:

u = \frac{1}{2}\varepsilon_0 E^2

(energy per unit volume).

2 Volume between plates:

V = A \cdot d

3 Total stored energy:

U = u \times V = \left(\frac{1}{2}\varepsilon_0 E^2\right)(A d) = \frac{1}{2}\varepsilon_0 E^2 A d

4 Match Option (3).

🛡️

Why You Can 100% Trust This Shortcut: Canonical field energy formulation of Maxwell-Poynting electrodynamics.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Expressing Energy via Circuit Capacitance

The electrostatic potential energy $U$ stored in a charged capacitor of capacitance $C$ with potential difference $V_0$ across its plates is:

U = \frac{1}{2} C V_0^2

Step 2

Substituting Field Variables for a Parallel Plate Capacitor

For an ideal parallel plate capacitor in vacuum: - Capacitance: $C = \frac{\varepsilon_0 A}{d}$ - Potential difference: $V_0 = E \cdot d$

U = \frac{1}{2} \left(\frac{\varepsilon_0 A}{d}\right) (E d)^2 = \frac{1}{2} \left(\frac{\varepsilon_0 A}{d}\right) (E^2 d^2)

Step 3

Simplifying to Final Expression

Canceling one factor of plate separation $d$ :

U = \frac{1}{2} \varepsilon_0 E^2 A d

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

This is the electrostatic energy density $u$ (energy per unit volume, $\text{J/m}^3$ ), not the total energy in Joules.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing energy density with total energy.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Lacks the essential factor of $1/2$ and has linear $E$ instead of quadratic $E^2$ .

⚠️

Student Fallacy (Why candidates pick this trap): Dimensionally inconsistent formula.

3 3

✓ 100% Correct

Verdict & Scientific Reason:

Exact total energy stored in the electric field of the capacitor: $U = \frac{1}{2}\varepsilon_0 E^2 A d$ .

💡

Why this is airtight: None; rigorous capacitive energy derivation.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Inverts permittivity $\varepsilon_0$ to denominator and misses $1/2$ .

⚠️

Student Fallacy (Why candidates pick this trap): Dimensionally incorrect equation.

⚠️

NTA Trap Alert: Energy vs. Energy Density Confusion Trap

NTA included Option (1) $\frac{1}{2}\varepsilon_0 E^2$ , which is energy density ( $u = U/V$ ). Students who memorize $\frac{1}{2}\varepsilon_0 E^2$ without tracking units frequently pick Option (1).

🛡️ How to avoid the -1 mark: Check dimensions: Total energy MUST have dimensions of work/energy (

\text{Joules}

), requiring multiplication by volume

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📖

Core NEET Syllabus Standard

NCERT Physics · Electrostatic Potential and Capacitance Standard Benchmark

Core Scientific Principle Tested:

"The total energy stored in a parallel plate capacitor is the product of electrostatic energy density and field volume: $U = u \times (Ad) = \frac{1}{2}\varepsilon_0 E^2 Ad$ ."

Syllabus Focus: Energy Stored in a Capacitor

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 21 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Energy = Energy Density × Volume

Step-by-Step Rigorous Workflow & Mathematical Proof

Expressing Energy via Circuit Capacitance

Substituting Field Variables for a Parallel Plate Capacitor

Simplifying to Final Expression

360° Option Elimination Engine Key Feature

NTA Trap Alert: Energy vs. Energy Density Confusion Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Electrostatic Potential and Capacitance

Electrostatic Energy Ratio in a Series-Parallel Capacitor Network

Path-Independence of Electrostatic Work & Potential of a Uniformly Charged Sphere

Electrostatic Shielding and Cavity Field with Interior Point Charge

Speed of an Attracted Point Charge Reaching the Surface of a Charged Insulating Sphere

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