EXPLANATIONS FOR CHALLENGES 1 AND 2 (written in separate document for
clarity)
CHALLENGE #1:
According to the data in the table above, the general trend is that as the magnitude of the charge on the two
objects (q1 and q2) increases, the electrostatic force (Felect) increases. This shows that the relationship between
both quantities is one of direct proportionality.
While q2 remains constant, we find that when q1 is doubled (changes from 0.000005C to 0.00001C), F elect =1.1N
becomes 2.1N (approximately double of 1.1N). When q1 is tripled (changes from 0.000005C to 0.000015C), F elect
=1.1N becomes 3.2N (approximately triple of 1.1N). When q1 is quadrupled (changes from 0.000005C to
0.00002C), Felect =1.1N becomes 4.2N (approximately quadruple of 1.1N).
Similarly, while q1 remains constant, we find that when q2 is doubled (changes from 0.0002C to 0.0004C), F elect
=4.2N becomes 8.5N (approximately double of 4.2N). When q2 is tripled (changes from 0.0002C to 0.0006C),
Felect =4.2N becomes 12.7N (approximately triple of 4.2N).
WHEN BOTH q1 and q2 CHANGE
Initially, q1 = 0.000005C and q2 = 0.0002C and Felect = 1.1N. When q1 becomes 0.00002C (q1 is quadrupled)
and q2 becomes 0.0006C (q2 is tripled), we see that Felect is now 12.7N, approximately 12 times its original value
of 1.1N. This takes the factors four and three respectively and multiplies them together, increasing 1.1N by a
factor of 12.
Initially, when q1 = 0.00001C and q2 = 0.0002C, F elect = 2.1N. When q1 becomes 0.00002C (q1 is doubled) and
q2 becomes 0.0004C (q2 is doubled), we see that Felect is now 8.5N, approximately 4 times its original value of
2.1N. This takes the factors two and two respectively and multiplies them together, increasing 2.1 by a factor of 4.
These analyses show that the product of the magnitudes of the charges of objects (q1 and q2) is directly
proportional to the electrostatic force (Felect). If q1 and q2 are increased/decreased by respective factors, the
electrostatic force Felect will increase/decrease by the same factors.
CHALLENGE #2:
According to the data in the table above, the general trend is that as separation distance(d) increases, the
electrostatic force (Felect) decreases. This allows us first understand that the relationship between both quantities
is one of inverse proportionality
Through mathematical analysis, we find that when d is doubled, Felect becomes approximately a quarter of its
original magnitude. This hints at a relationship involving the square since 4 is 2 squared. When d=1, Felect =293N.
When d is doubled and becomes d=2, Felect is divided by 4, becoming about a quarter of its original value and Felect
= 78N. When d is again doubled to become d=4, Felect again is divided by 4, becoming a fourth of 78N,
approximately 18.9N. Doubling the distance again to make d=8, gives Felect =4.6N meaning that 18.9N gets
divided by 4, becoming a fourth of its previous value.
Through further mathematical analysis, we find that when d is tripled, Felect becomes approximately a ninth of its
original magnitude. This hints at a relationship involving the square since 9 is 3 squared. When d=1, Felect =293N.
When d is tripled and becomes d=3, Felect is divided by 9, becoming about a ninth of its original value and Felect =
34N. When d is again tripled to become d=9, Felect again is divided by 9, becoming a ninth of 34N, approximately
3.7N.
Lastly, when d is quadrupled from d=1 to d=4, the force becomes a sixteenth of its original magnitude. This hints
at a relationship involving the square since 16 is 4 squared. Felect reduced from 293N to 18.9N (293 divided by
16).
These analyses inform us of an inversely proportional square relationship. When distance (d) increases by a
factor, electrostatic force (Felect) decreases by the square of that factor.