Physics Electrostatics DUHS 2022
PMDC Verified Question 82 of 131
Q.142 Two similar point charges, each of 1 coulomb, placed in free space 1m apart, repel each other with a force of:
A
\( 8.85 \times 10^{-12} \text{ N} \)
B
\( 1.602 \times 10^{-19} \text{ N} \)
C
1 N
D
\( 9 \times 10^9 \text{ N} \)
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Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( 9 \times 10^9 \text{ N} \)
1. Concept:

This setup represents the foundational definition of Coulomb's constant \( k \). Finding the force between two exactly 1 Coulomb charges separated by exactly 1 meter effectively outputs the constant itself.

2. Formula:

$$ F = k \frac{q_1 q_2}{r^2} $$

3. Solution:

  • Given charges: \( q_1 = 1 \text{ C} \), \( q_2 = 1 \text{ C} \).


  • Given distance: \( r = 1 \text{ m} \).


  • Substitute: \( F = (9 \times 10^9) \frac{1 \times 1}{1^2} \).


  • Result: \( F = 9 \times 10^9 \text{ N} \).


4. Why other options are incorrect:

Option A is the permittivity of free space (\( \epsilon_0 \)), not the force constant. Option B is the charge of a single electron. Option C naively assumes the variables multiply without the \( k \) constant multiplier.

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