Coulomb's Law

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Coulomb's Law

 
 
Charged objects attract or repel with a force (F_elect) that is directly proportional to the quantity of charge (Q₁ and Q₂) on either of the objects and inversely proportional to the square of the distance (d) between the object's centers. This relationship is known as Coulomb's Law.

To say the force (F_elect) is directly proportional to the quantity of charge (Q) means that an increase in a Q value causes an increase in the F value. And a decrease in Q causes a decrease in F. But it also means that the factor by which a Q value is changed is equal to the factor by which the F_elect is changed. So a doubling of Q₁ causes a doubling of F_elect. And a tripling of Q₁ causes a tripling of F_elect. A halving of Q₁ causes a halving of F_elect. If both Q₁ and Q₂ are changed, then you must change the F twice – once for each Q change.

In Example 1, the value of Q₁ is tripled and the value of Q₂ is halved. So to determine the new F_elect, take the original F_elect of 32 units and triple it (for the Q₁ change) and halve it (for the Q₂ change). The new force is 48 units.

To say that the force (F_elect) is inversely proportional to the square of the distance (d) means that an increase in d causes a decrease in the F_elect value. And a decrease in d causes an increase in F_elect. That's the "inverse" part of the statement. But it also means that the factor by which the F_elect is decreased is the square of the factor by which the d is increased. So a doubling of d causes F to decrease by a factor of 4 (2²). A tripling of d causes F to decrease by a factor of 9 (3²). And a halving of d causes the F to increase by a factor of 4.

In Example 2, the value of d is one-third the original value. Since d decreases by a factor of 3, F_elect increases by a factor of 9. So to determine the new F_elect, take the original F_elect of 32 units and multiply it by 9.

In Example 3, Q₁, Q₂, and d are all changed. So the original force of 32 units must be changed three times … once for each variable. Since Q₁ is quadrupled, F must be multiplied by 4. Since Q₂ is tripled, F must be multiplied by 3. And since d was doubled, F must be divided by 4. Use your calculator to determine that the new force is 96 units.

These three examples illustrate how Coulomb's Law can be used to determine a new force. I’m Mr. H, letting you know that … You got this!
 

 
 

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