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)
The electric force exerted by these two charges on q3 is -2.44 kC.
To find the electric force exerted by these two charges on a third charge, we can use Coulomb's Law.
Coulomb's Law states that the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for electric force (F) is given by:
F = k * (|q1| * |q2|) / r^2
where:
k is Coulomb's constant (8.99 × 10^9 N·m^2/C^2),
|q1| and |q2| are the magnitudes of the two charges (2.00 × 10^(-9) C and 3.00 × 10^(-9) C, respectively),
r is the distance between the charges (0.020 m and 0.040 m, respectively).
Let's calculate it step by step.
Step 1: Calculate the distance between q1 and q3.
The distance between q1 and q3 is 0.020 m.
Step 2: Calculate the distance between q2 and q3.
The distance between q2 and q3 is 0.040 m.
Step 3: Calculate the electric force between q1 and q3.
F1 = k * (|q1| * |q3|) / (0.020)^2
Substituting the values:
F1 = (8.99 × 10^9 N·m^2/C^2) * (2.00 × 10^(-9) C * 5.00 × 10^(-9) C) / (0.020 m)^2
F1 = (8.99 × 10^9 N·m^2/C^2) * (10^(-18) C^2) / (4 × 10^(-4) m^2)
F1 = (8.99 × 10^(9-18-4)) N
F1 = (8.99 × 10^(-13)) N
Step 4: Calculate the electric force between q2 and q3.
F2 = k * (|q2| * |q3|) / (0.040)^2
Substituting the values:
F2 = (8.99 × 10^9 N·m^2/C^2) * (3.00 × 10^(-9) C * 5.00 × 10^(-9) C) / (0.040 m)^2
F2 = (8.99 × 10^9 N·m^2/C^2) * (15 × 10^(-18) C^2) / (16 × 10^(-4) m^2)
F2 = (8.99 × 10^(9-18-4)) N
F2 = (8.99 × 10^(-13)) N
Step 5: Find the net electric force on q3.
The electric forces F1 and F2 act on q3 in opposite directions since q1 and q2 have opposite charges. Therefore, we subtract their magnitudes.
Net force on q3 = |F1| - |F2|
Net force on q3 = (8.99 × 10^(-13)) N - (8.99 × 10^(-13)) N
Net force on q3 = 0 N
The net electric force exerted by these two charges on a third charge q3 located at the origin is 0 N.
To find the electric force exerted by the two charges on the third charge, you can use Coulomb's law. Coulomb's law states that the electric force between two charges is directly proportional to the product of the charges 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 electric force
k is the Coulomb's constant, k = 8.99 × 10^9 N·m^2/C^2
|q1 * q2| is the product of the magnitudes of the charges q1 and q2
r^2 is the square of the distance between the charges
In this case, q1 = 2.00 × 10^-9 C, q2 = -3.00 × 10^-9 C, and q3 = 5.00 × 10^-9 C. The distance between q1 and q3 (from the origin) is 0.020 m and the distance between q2 and q3 is 0.040 m.
First, calculate the electric force between q1 and q3:
F1 = (k * |q1 * q3|) / r1^2
F1 = (8.99 × 10^9 N·m^2/C^2 * |2.00 × 10^-9 C * 5.00 × 10^-9 C|) / (0.020 m)^2
Next, calculate the electric force between q2 and q3:
F2 = (k * |q2 * q3|) / r2^2
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, add the two forces together to get the total electric force:
F_total = F1 + F2
Calculate each term separately and then add them together to find the total electric force exerted by the charges on the third charge at the origin.