Two charges are located on the positive x-axis of a coordinate system. Charge q1 = 2.00 × 10−9C, and it is 0.020 m from the origin. Charge q 2 = –3.00 × 10 −9 C, and it is 0.040 m from the origin. What is the electric force exerted by these two charges on a third charge, q 3 = 5.00 × 10−9, located at the origin? (kC = 8.99 × 109 N•m2/C2)
1
To find the electric force exerted on charge q3 by charges q1 and q2, we can use Coulomb's law, which states that the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Let's break down the problem step by step:
Step 1: Calculate the distance between q1 and q3.
The distance between q1 and q3 is the same as the distance between q1 and the origin since q3 is located at the origin. Therefore, the distance between q1 and q3 is given as 0.020 m.
Step 2: Calculate the distance between q2 and q3.
Again, since q3 is located at the origin, the distance between q2 and q3 is the same as the distance between q2 and the origin, which is 0.040 m.
Step 3: Calculate the electric force exerted on q3 by q1.
Using Coulomb's law, the formula for the electric force (F) can be written as:
F1 = k * (|q1| * |q3|) / r1^2
where:
- k is the Coulomb's constant (k = 8.99 × 10^9 N•m^2/C^2)
- |q1| and |q3| are the magnitudes of the charges (2.00 × 10^(-9) C and 5.00 × 10^(-9) C, respectively)
- r1 is the distance between q1 and q3 (0.020 m)
Substituting the given values into the formula, we have:
F1 = (8.99 × 10^9 N•m^2/C^2) * ((2.00 × 10^(-9) C) * (5.00 × 10^(-9) C)) / (0.020 m)^2
Step 4: Calculate the electric force exerted on q3 by q2.
Using the same formula, we can find the force (F2) exerted on q3 by q2:
F2 = k * (|q2| * |q3|) / r2^2
where:
- |q2| is the magnitude of charge q2 (3.00 × 10^(-9) C)
- r2 is the distance between q2 and q3 (0.040 m)
Substituting the given values, we have:
F2 = (8.99 × 10^9 N•m^2/C^2) * ((3.00 × 10^(-9) C) * (5.00 × 10^(-9) C)) / (0.040 m)^2
Step 5: Calculate the net electric force on q3.
To find the net electric force (Fnet) on q3, we need to sum up the forces F1 and F2:
Fnet = F1 + F2
Calculate F1:
F1 = (8.99 × 10^9 N•m^2/C^2) * ((2.00 × 10^(-9) C) * (5.00 × 10^(-9) C)) / (0.020 m)^2
Calculate F2:
F2 = (8.99 × 10^9 N•m^2/C^2) * ((3.00 × 10^(-9) C) * (5.00 × 10^(-9) C)) / (0.040 m)^2
Finally, calculate the net force:
Fnet = F1 + F2
By following these steps and performing the calculations, you can find the electric force exerted by these two charges on the third charge at the origin.
To find the electric force exerted by two charges on a third charge, we can use Coulomb's Law, which states that the electric force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the electric force,
k is the electrostatic constant, which is given as k = 8.99 × 10^9 N•m^2/C^2,
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
In this case, we have two charges, q1 and q2, located on the positive x-axis. The distance between q1 and q2 is the difference between their distances from the origin. Therefore, we can calculate the distance between q1 and q2 as:
r = |r2 - r1| = |0.040 m - 0.020 m| = 0.020 m
Now we can plug in the values into the formula:
F = (8.99 × 10^9 N•m^2/C^2) * ((2.00 × 10^(-9) C) * (3.00 × 10^(-9) C)) / (0.020 m)^2
Calculating the above expression will give us the magnitude of the electric force exerted by the two charges on the third charge, q3.