The sum of two point charges is 6µC. They attract each other with a force of 0.9N, when kept 40cm apart. Calculate the charges.
To calculate the charges of the two point charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Step 1: Determine the given information:
- The sum of the two point charges is 6 µC.
- The force between the two charges is 0.9 N.
- The distance between the charges is 40 cm.
Step 2: Convert the distance to meters:
Since Coulomb's Law requires the distance to be in meters, we need to convert 40 cm to meters. There are 100 centimeters in 1 meter, so 40 cm is equal to 40/100 = 0.4 meters.
Step 3: Apply Coulomb's Law:
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
- F is the force between the charges
- k is the electrostatic constant (9 × 10^9 N*m^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges
Plugging in the known values:
0.9 N = (9 × 10^9 N*m^2/C^2) * ((q1 + q2) / (0.4 m)^2)
Step 4: Simplify the equation:
0.9 N = (9 × 10^9 N*m^2/C^2) * (6 µC / (0.4 m)^2)
Step 5: Solve for the charges:
To solve for the charges, we can rearrange the equation to solve for (q1 + q2):
(q1 + q2) = (0.9 N * (0.4 m)^2) / (9 × 10^9 N*m^2/C^2)
(q1 + q2) = 0.0016 C
Since we know that the sum of the charges is 6 µC, we can set up another equation:
q1 + q2 = 6 × 10^-6 C
Substituting the value of (q1 + q2) from the previous equation:
0.0016 C = 6 × 10^-6 C
Step 6: Solve for the individual charges:
(q1 + q2) = 0.0016 C
6 × 10^-6 C = 0.0016 C
Simplifying the equation:
(q1 + q2) = 0.0016 C
q1 + q2 = 0.0016 C * (1 / 6 × 10^-6)
q1 + q2 = 0.2667 C
Since q1 + q2 = 0.2667 C and q1 + q2 = 0.0016 C, we can solve for q1 and q2:
q1 = 0.2667 C - 0.0016 C
q1 = 0.2651 C
q2 = 0.0016 C
Therefore, one of the charges (q1) is approximately 0.2651 C, and the other charge (q2) is approximately 0.0016 C.
To calculate the charges of the two point charges, we can use Coulomb's Law, which states that the force of attraction or repulsion between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb's Law can be expressed as:
F = k * (|q1| * |q2|) / r^2
where F is the force, k is Coulomb's constant, |q1| and |q2| are the magnitudes of the two charges, and r is the distance between them.
We are given that the force, F, is 0.9N and the distance, r, is 40cm.
First, let's convert the distance to meters:
r = 40cm = 0.4m
Next, let's rearrange the formula to solve for the magnitudes of the charges:
|q1| * |q2| = (F * r^2) / k
Now, we need to substitute the values of the given variables into the formula:
|q1| * |q2| = (0.9N * (0.4m)^2) / (9 x 10^9 Nm^2/C^2)
Simplifying the equation:
|q1| * |q2| = (0.9N * (0.16m^2)) / (9 x 10^9 Nm^2/C^2)
|q1| * |q2| = 0.144C / 9 x 10^9 Nm^2/C^2
|q1| * |q2| = 1.6 x 10^-11 C
Now, we need to find two numbers whose product is 1.6 x 10^-11 C. Since the sum of the two charges is 6µC (which is 6 x 10^-6 C), we can solve for the charges by trial and error or by finding the factors of 1.6 x 10^-11 C and testing them until their sum is 6 x 10^-6 C.
Let's consider some possible values for |q1| and |q2|:
|q1| = 1 x 10^-11 C and |q2| = 1.6 x 10^-11 C
|q1| * |q2| = (1 x 10^-11 C) * (1.6 x 10^-11 C)
|q1| * |q2| = 1.6 x 10^-22 C^2
Since 1.6 x 10^-22 C^2 is not equal to 1.6 x 10^-11 C, this is not the correct combination of charges.
Let's consider another possible combination:
|q1| = 2 x 10^-11 C and |q2| = 8 x 10^-12 C
|q1| * |q2| = (2 x 10^-11 C) * (8 x 10^-12 C)
|q1| * |q2| = 16 x 10^-23 C^2
|q1| * |q2| = 1.6 x 10^-22 C^2
This combination satisfies the equation, so the charges are |q1| = 2 x 10^-11 C and |q2| = 8 x 10^-12 C.
Therefore, the charges of the two point charges are 2 x 10^-11 C and 8 x 10^-12 C, respectively.
.9=kq1(6-q1)e-6/.4^2
solve for q1. notice it is a quadratic, use the quadratic equation.
Q2 = [6*10^-6 Coulombs + Q1] because attracting one must be + and the other -
.9 = k Q1Q2/0.40^2
.9*.16 = 9*10^9 (Q1)(-6*10^-6+Q1)
16*10^-12 = -6*10^-6 Q1 +Q1^2
Q1 ^2 - 6*10^-6 Q1 - 16 *10^-12 = 0
pretend it is Q1^2 - 6 Q1 - 16 =0
(Q1 - 8)(Q1+2) = 0
so one is 8 * 10^-6 then the other is -2 * 10^-6