Charge q₁ = 1.4-10" C is placed at the origin. Charges 4-1.8-10 C and 4, 2.1-10 C are placed at points (0.18 m,0 m) and (0 m,0.24 m), respec- tively, as shown in the figure. Determine the net electrostatic force (magnitude and direction) on charge q.
simple steps
To determine the net electrostatic force on charge q, we need to calculate the individual forces between q and the other charges, and then add them together.
1. Calculate the force between q and the charge at (0.18 m, 0 m):
Using Coulomb's Law, the formula for the electrostatic force between two charges is F = k * (q1 * q2) / r^2,
where k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2) and r is the distance between the charges.
F1 = (9 x 10^9 Nm^2/C^2) * ((1.4 x 10^-10 C) * (4 x 10^-10 C)) / (0.18 m)^2
= 8.4 N (towards the origin)
2. Calculate the force between q and the charge at (0 m, 0.24 m):
Again, using Coulomb's Law:
F2 = (9 x 10^9 Nm^2/C^2) * ((1.4 x 10^-10 C) * (2.1 x 10^-10 C)) / (0.24 m)^2
= 6.4 N (towards the origin)
3. Add the forces together to find the net force:
The net force is the vector sum of the individual forces. In this case, since both forces are pointing towards the origin, we can simply add their magnitudes:
Net force = F1 + F2
= 8.4 N + 6.4 N
= 14.8 N
Therefore, the net electrostatic force on charge q is 14.8 N, directed towards the origin.
1. Calculate the distances between charge q₁ and each of the other charges.
- Distance between q₁ and charge (4-1.8-10 C):
-√((0.18 - 0)² + (0 - 0)²) = 0.18 m
- Distance between q₁ and charge (4, 2.1-10 C):
-√((0 - 0)² + (0.24 - 0)²) = 0.24 m
2. Calculate the electrostatic force between charge q₁ and each of the other charges using Coulomb's Law:
- Force between q₁ and charge (4-1.8-10 C):
F₁ = (9 × 10^9 Nm²/C²) × ((1.4 × 10^-10 C) × (4 × 10^-10 C) / (0.18 m)²)
- Force between q₁ and charge (4, 2.1-10 C):
F₂ = (9 × 10^9 Nm²/C²) × ((1.4 × 10^-10 C) × (4 × 10^-10 C) / (0.24 m)²)
3. Calculate the net force acting on charge q₁ by summing up the individual forces:
- Net Force = F₁ + F₂
4. Calculate the magnitude and direction of the net force:
- Magnitude: Take the absolute value of the net force. |Net Force|
- Direction: Determine the direction of the net force by considering the signs of the individual forces. If the net force is positive, the direction will be towards the positive charges. If the net force is negative, the direction will be towards the negative charges.
To determine the net electrostatic force on charge q₁, we need to find the individual forces between q₁ and the two other charges, and then add them vectorially.
Here are the steps to find the net electrostatic force:
Step 1: Calculate the distance between charge q₁ and each of the other charges.
- The distance between q₁ and the charge 4-1.8-10 C is 0.18 m.
- The distance between q₁ and the charge 4, 2.1-10 C is 0.24 m.
Step 2: Calculate the magnitude of the force between q₁ and each of the other charges using Coulomb's Law equation:
- The force between q₁ and the charge 4-1.8-10 C is given by F₁ = (k * |q₁| * |q₂|) / r₁², where k is the electrostatic constant (9 * 10^9 N*m²/C²), |q₁| is the magnitude of charge q₁, |q₂| is the magnitude of the charge 4-1.8-10 C, and r₁ is the distance between the charges.
- The force between q₁ and the charge 4, 2.1-10 C is given by F₂ = (k * |q₁| * |q₃|) / r₂², where |q₃| is the magnitude of the charge 4, 2.1-10 C, and r₂ is the distance between the charges.
Step 3: Find the direction of each force. The direction is determined by the relative positions of the charges and can be determined by using the vector notation.
- The force F₁ between q₁ and the charge 4-1.8-10 C is repulsive since both charges have the same sign (+ and -).
- The force F₂ between q₁ and the charge 4, 2.1-10 C is attractive since the charges have opposite signs (+ and -).
Step 4: Add the vector forces F₁ and F₂ to find the net force (magnitude and direction) on charge q₁. Since F₁ and F₂ have different directions, we can add them using vector addition.
Step 5: Determine the magnitude and direction of the net force. The magnitude of the net force can be found by taking the vector sum of F₁ and F₂ (let's call it F_net), and the direction of F_net will be the same as the direction of the resultant vector (opposite charge).
Following these steps, you can find the net electrostatic force (magnitude and direction) on charge q₁.