Coulomb's Law
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Coulomb's Law
Video Transcript
Charged objects attract or repel with a force (F
elect) that is directly proportional to the quantity of charge (Q
1 and Q
2) 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 Q
1 causes a doubling of F
elect. And a tripling of Q
1 causes a tripling of F
elect. A halving of Q
1 causes a halving of F
elect. If both Q
1 and Q
2 are changed, then you must change the F twice – once for each Q change.
In Example 1, the value of Q
1 is tripled and the value of Q
2 is halved. So to determine the new F
elect, take the original F
elect of 32 units and triple it (for the Q
1 change) and halve it (for the Q
2 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 (2
2). A tripling of d causes F to decrease by a factor of 9 (3
2). 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, Q
1, Q
2, and d are all changed. So the original force of 32 units must be changed three times … once for each variable. Since Q
1 is quadrupled, F must be multiplied by 4. Since Q
2 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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