Q.43 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 43 Solution

Topic: Electrostatic Potential and Capacitance · Official NTA Booklet Code G5

Question

An electric dipole is placed as shown in the figure. The electric potential (in 10² V) at point P due to the dipole is (ε₀ = permittivity of free space and 1/(4πε₀) = K): [charges −q and +q are 3 cm on either side of O; P is 5 cm from O]

✓

Verified Against NTA Final Answer Key

Option (2) : (3/8) q K

📚 Electrostatic Potential and Capacitance Easy

📋 Given Parameters & Problem Setup

Center-to-charge distance (a) 3 cm (charges at -3 cm and +3 cm)

Center-to-point P distance (r) 5 cm on positive axis

Distance from +q to P (r₊) 5 cm - 3 cm = 2 cm = 2 × 10⁻² m

Distance from -q to P (r₋) 5 cm + 3 cm = 8 cm = 8 × 10⁻² m

Coulomb constant (K) 1 / (4πε₀)

Target units Potential expressed in 10² V

⚡

The 30-Second Exam Hall Shortcut: ⚡ Exact Distance Reciprocal Difference: V = Kq [1/r₊ - 1/r₋]

⏱️ Save ~40 seconds

r₊ = 2 cm and r₋ = 8 cm. In meters: 1/0.02 - 1/0.08 = 50 - 12.5 = 37.5. In units of 10² V: 37.5 / 100 = 3/8! Potential = (3/8) qK in 15 seconds!

1 Find distance from each charge to observation point P:

2 - From +q: r₊ = 5 cm - 3 cm = 2 cm = 2 × 10⁻² m.

3 - From -q: r₋ = 5 cm + 3 cm = 8 cm = 8 × 10⁻² m.

4 Use exact principle of superposition for potential: V = K q / r₊ - K q / r₋.

5 Factor out K q: V = K q [ 1/(2 × 10⁻²) - 1/(8 × 10⁻²) ] = 10² K q [ 1/2 - 1/8 ].

6 Evaluate bracket: 1/2 - 1/8 = (4 - 1) / 8 = 3/8.

7 Thus V = (3/8) q K × 10² V. The question asks for potential in units of 10² V.

8 Directly select Option (2) (3/8) q K!

🛡️

Why You Can 100% Trust This Shortcut: Electrostatics · Superposition Principle for Potential (Electric potential is a scalar sum: V = Σ K q_i / r_i, valid for all separations without dipole approximations).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Identification of Charge Locations and Observation Point

The electric dipole consists of charges -q and +q placed symmetrically along the x-axis around the origin 0: charge -q is at x = -3 cm, and charge +q is at x = +3 cm. Point P lies on the positive x-axis at x = +5 cm.

x_{-q} = -3\text{ cm}, \quad x_{+q} = +3\text{ cm}, \quad x_P = +5\text{ cm}

Step 2

Calculation of Geometric Distances to Point P

Calculate the distances r₊ and r₋ from charges +q and -q to point P in meters:

\begin{aligned} r_+ &= 5\text{ cm} - 3\text{ cm} = 2\text{ cm} = 2 \times 10^{-2}\text{ m} \\[6pt] r_- &= 5\text{ cm} - (-3\text{ cm}) = 8\text{ cm} = 8 \times 10^{-2}\text{ m} \end{aligned}

Step 3

Superposition of Scalar Potentials

By the principle of superposition, the net electrostatic potential V at point P is the algebraic scalar sum of the potentials due to both individual point charges:

V = K \left( \frac{+q}{r_+} + \frac{-q}{r_-} \right) = K q \left( \frac{1}{2 \times 10^{-2}} - \frac{1}{8 \times 10^{-2}} \right)

Step 4

Factoring Out the 10² Scale Factor

Factor out 10² from the denominator into the numerator:

V = K q \times 10^2 \left( \frac{1}{2} - \frac{1}{8} \right) = K q \times 10^2 \left( \frac{4 - 1}{8} \right) = \frac{3}{8}\, q K \times 10^2\text{ V}

Step 5

Expression in Target Units of 10² V

The question asks for the potential expressed in units of 10² V:

\frac{V}{10^2\text{ V}} = \left(\frac{3}{8}\right) q K

⭐

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:

Inverted fraction (8/3 instead of 3/8).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate inverted the numerator and denominator.

2 (2)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate value: 1/2 - 1/8 = 3/8.

💡

Why this is airtight: None. Candidate correctly computed exact distances without short-dipole approximations.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Addition error in numerator (4 + 1 = 5 instead of 4 - 1 = 3).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate added the potentials instead of subtracting the negative charge’s potential.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Inverted sum error.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate inverted the sum 5/8.

⚠️

NTA Trap Alert: Applying the Far-Field Short Dipole Formula V = K p / r²

The short-dipole approximation V = K p / r² is valid only when r >> a. Here, r = 5 cm and a = 3 cm, so r is comparable to a! Applying the far-field formula gives V = K(2qa)/r² = K q(6)/25 = 0.24 qK, which yields no matching answer.

🛡️ How to avoid the -1 mark: When distances are comparable to dipole size (5 cm vs 3 cm), ALWAYS use exact point-charge superposition: V = Kq(1/r₊ - 1/r₋).

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Electrostatic Potential and Capacitance Standard Benchmark

Core Scientific Principle Tested:

"The exact axial potential is V = K q [1/(r - a) - 1/(r + a)]."

Syllabus Focus: Electric Potential due to an Electric Dipole

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 200-minute timed NTA simulator.

Launch NEET 2023 CBT Test →

← Previous (Q.42) All Physics Questions Grid Next (Q.44) →

🔗 Related Questions — Electrostatic Potential and Capacitance

All 19 Electrostatic Potential and Capacitance PYQs →

NEET 2026 Q9

Electrostatic Energy Ratio in a Series-Parallel Capacitor Network

View Solution →

NEET 2026 Q21

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

View Solution →

NEET 2026 Q33

Electrostatic Shielding and Cavity Field with Interior Point Charge

View Solution →

NEET 2026 Q34

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

View Solution →

Spotted a mistake in this solution? Report an error ([email protected])

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2023 question papers and NEET answer keys for private study, research, and non-commercial educational practice under Fair Dealing (Section 52(1)(a) of the Indian Copyright Act, 1957). Not affiliated with or endorsed by NTA or NMC.

NEET 2023 Physics Question 43 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Exact Distance Reciprocal Difference: V = Kq [1/r₊ - 1/r₋]

Step-by-Step Rigorous Workflow & Mathematical Proof

Identification of Charge Locations and Observation Point

Calculation of Geometric Distances to Point P

Superposition of Scalar Potentials

Factoring Out the 10² Scale Factor

Expression in Target Units of 10² V

360° Option Elimination Engine Key Feature

NTA Trap Alert: Applying the Far-Field Short Dipole Formula V = K p / r²

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

Solve 4 NEET Questions a Day — One per Subject