Bot GPT 4-o mini The magnitude of electrical charge on objects directly affects the electric force between them according to Coulomb's Law. Coulomb's Law states that the electric force (\( F \)) between two point charges is directly proportional to the product of the magnitudes of the charges (\( q_1 \) and \( q_2 \)) and inversely proportional to the square of the distance (\( r \)) between them. The law can be expressed mathematically as:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
Where:
- \( F \) is the magnitude of the electric force between the charges,
- \( k \) is Coulomb's constant (\( \approx 8.99 \times 10^9 , \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the two charges,
- \( r \) is the distance between the centers of the two charges.
Key points to understand from this equation:
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Proportionality to Charge Magnitudes: The electric force increases as the magnitude of either charge increases. For example, if you double the magnitude of one charge while keeping the other constant, the electric force will also double.
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Inverse Square Relationship: The force decreases with the square of the distance between the charges. If the distance \( r \) is doubled, the force becomes one-fourth of its original value.
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Direction of Force: The electric force is attractive if the charges are opposite (one positive, one negative) and repulsive if the charges are the same (both positive or both negative).
In summary, the greater the magnitudes of the charges, the stronger the electric force between them, while the force weakens as the distance separating them increases.
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