the electric force between Q1 and Q2 is 1.2 going to left. determine the distance between the two charges, and the electric field, E1 and E2, of the electric charges if Q1 is 6 x 10^-6 C, Q2 is 4 x 10^-6 and test charge of +1 x 10^-6 C
E1=kq1/x^2 solve for x
E2=kq2/(d-x)^2 solve for distance d.
I have no idea what you are doing with the test charge.
To determine the distance between the two charges (Q1 and Q2) and the electric fields (E1 and E2), we can use Coulomb's Law. Coulomb's Law 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.
Step 1: Determine the electric force between Q1 and Q2.
The electric force between two charges can be calculated using the formula:
F = k * |Q1| * |Q2| / r^2
where F is the electric force, k is the electrostatic constant (k = 9 × 10^9 N m^2/C^2), |Q1| and |Q2| are the magnitudes of the charges, and r is the distance between them.
Given:
- Q1 = 6 × 10^-6 C (charge of Q1)
- Q2 = 4 × 10^-6 C (charge of Q2)
- F = -1.2 (electric force between Q1 and Q2)
We can rearrange the formula to solve for r:
r = √(k * |Q1| * |Q2| / |F|)
Substituting the given values:
r = √((9 × 10^9 N m^2/C^2) * (6 × 10^-6 C) * (4 × 10^-6 C) / 1.2)
Calculating the expression inside the square root:
r = √(1.8 × 10^4 m^2)
Simplifying the expression:
r = 134.16 m
Therefore, the distance between the two charges (Q1 and Q2) is approximately 134.16 meters.
Step 2: Determine the electric fields (E1 and E2) of the charges.
The electric field, E, at any point in space due to a charge can be calculated using the formula:
E = k * |Q| / r^2
where E is the electric field, k is the electrostatic constant (k = 9 × 10^9 N m^2/C^2), |Q| is the magnitude of the charge, and r is the distance between the charge and the point of interest.
For Q1:
- |Q| = 6 × 10^-6 C
- r = 134.16 m (distance between Q1 and Q2)
Calculating E1:
E1 = (9 × 10^9 N m^2/C^2) * (6 × 10^-6 C) / (134.16 m)^2
Simplifying the expression:
E1 ≈ 3.14 N/C
For Q2:
- |Q| = 4 × 10^-6 C
- r = 134.16 m (distance between Q1 and Q2)
Calculating E2:
E2 = (9 × 10^9 N m^2/C^2) * (4 × 10^-6 C) / (134.16 m)^2
Simplifying the expression:
E2 ≈ 2.09 N/C
Therefore, the electric field (E1) of Q1 is approximately 3.14 N/C, and the electric field (E2) of Q2 is approximately 2.09 N/C.