Respuesta :
Answer:
q(a) = 15 nC
q(b) = 10 nC
Explanation:
The distance between q(a) and q(b) is 5 cm
Also, q(a) + q(b) = 29 nC
Force between them, F(a,b) = 5.4*10^-4 N
Using Coulomb's law
F = kq1q2 / r², where
F = force between the charges
K = constant of proportionality
q1 = magnitude of first charge
q2 = magnitude of the second charge
r = distance between the charges
5.4*10^-4 = {8.99*10^9 * q(a)[25 - q(a)] *10^-18} / 0.05²
5.4*10^-4 = {8.99*10^9 * q(a)[25 - q(a)] *10^-18} / 0.0025
{8.99*10^9 * q(a)[25 - q(a)] *10^-18} = 5.4*10^-4 * 0.0025
{8.99*10^9 * q(a)[25 - q(a)] *10^-18} = 1.35*10^-6
q(a)[25 - q(a)] *10^-18 = 1.36*10^-6 / 8.99*10^9
q(a)[25 - q(a)] *10^-18 = 1.50*10^-16
q(a)[25 - q(a)] = 1.50*10^-16 * 10^18
q(a)[25 - q(a)] = 150
25q(a) - q(a)² = 150
q(a)² - 25q(a) + 150 = 0 solve using quadratic equation, we have
q(a) - 10 = 0
q(a) - 15 = 0
Since the question stated that q(a) had the higher charge, then q(a) = 15 nC and q(b) = 10 nC
Answer:
qA = 22.25 x 10^(-9) C
qB = 6.75 x 10^(9) C
Explanation:
We are given;
Sum of two charges = 29 nC
Thus, qA + qB = 29 x 10^(-9) C and
qA = 29 x 10^(-9)] - q2
Distance between 2 charges; r = 5cm = 0.05 m
Force between the 2 charges, F_(a,b) = 5.4 x 10^(-4) N
Now, from Coulomb's law, Force between charges is given as;
F = k•q1•q2/r², where
F = force between the charges
K = coulombs constant and has a value of 8.99 x 10^(9) N.m²/C²
q1 = qA= magnitude of charge A
q2 = qB = magnitude of charge B
r = distance between the charges
From earlier, we saw that;
qA = [29 x 10^(-9)] - qB
Plugging in the relevant values into the force equation, we have;
5.4 x 10^(-4) = [8.99 x 10^(9)•qA•qB]/0.05²
From earlier, we saw that;
qA = 29 x 10^(-9)] - qB
Thus,
5.4 x 10^(-4) = [8.99 x 10^(9)•(29 x 10^(-9)] - qB)•qB]/0.05²
5.4 x 10^(-4) = [8.99 x 10^(9)•(29 x 10^(-9)q2] - (qB)²)]/0.05²
5.4 x 10^(-4) x 0.05² = 260.71qB - 8.99 x 10^(9)(qB)²
8.99 x 10^(9)(qB)² - 260.71qB + 0.00000135 = 0
Finding the roots, we have;
qB = 6.75 x 10^(9) C or 22.25 x 10^(9) C
We know that;
qA = 29 x 10^(-9)] - qB
And from the question, we are told that qA has the greater charge, thus, we will use qB = 6.75 x 10^(9) C
So,
qA =
[29 x 10^(-9)] - 6.75 x 10^(9) = 22.25 x 10^(-9) C
