Three point charges are located at the corners of an equilateral triangle(q1=2microC,q2=-4microC).Calculate the resultant electric force on 7microC charge.
To calculate the resultant electric force on the 7 microC charge, we need to consider the forces exerted by each of the three charges on it and then find the vector sum of these forces.
Given:
Charge at point A (q1) = 2 microC
Charge at point B (q2) = -4 microC
Charge at point C = 7 microC
Step 1: Find the magnitude and direction of the force between q1 and C.
The magnitude of the force between two charges can be calculated using Coulomb's Law:
F₁ = k * (|q1| * |C|) / r₁²
Where:
F₁ is the magnitude of the force between q1 and C,
k is the electrostatic constant (k = 9 x 10^9 Nm²/C²),
|q1| and |C| are the magnitudes of the charges (2 microC and 7 microC, respectively),
r₁ is the distance between q1 and C.
Since it is an equilateral triangle, we can assume that the distance between q1 and C is equal to the side length of the triangle.
Step 2: Find the magnitude and direction of the force between q2 and C.
Using the same formula, we can calculate the force between q2 and C:
F₂ = k * (|q2| * |C|) / r₂²
where |q2| is 4 microC, |C| is 7 microC, and r₂ is the distance between q2 and C.
Step 3: Find the resultant force.
To find the resultant force, we need to find the vector sum of F₁ and F₂. Since the charges and distances are arranged symmetrically, the two forces will have the same magnitude but opposite directions. Therefore, the resultant force will be the vector sum of these two forces.
Resultant force = F₁ - F₂
Step 4: Calculate the magnitude and direction of the resultant force.
To find the magnitude of the resultant force, we can use the Pythagorean theorem:
|Resultant force| = √(F₁² + F₂²)
To find the direction, we can use trigonometry:
θ = atan(F₂ / F₁)
Now, let's calculate the values step by step.
Step 1: Calculate the magnitude of force F₁.
F₁ = (9 x 10^9 Nm²/C²) * ((2 x 10^-6 C) * (7 x 10^-6 C)) / r₁²
Since it is an equilateral triangle, the distance between q1 and C is equal to the side length of the triangle.
r₁ = side length of the triangle
Step 2: Calculate the magnitude of force F₂.
F₂ = (9 x 10^9 Nm²/C²) * ((4 x 10^-6 C) * (7 x 10^-6 C)) / r₂²
Step 3: Calculate the resultant force.
Resultant force = F₁ - F₂
Step 4: Calculate the magnitude and direction of the resultant force.
|Resultant force| = √(F₁² + F₂²)
θ = atan(F₂ / F₁)
By calculating these steps, we can find the resultant electric force on the 7 microC charge.
To calculate the resultant electric force on the 7 microC charge, we need to consider the forces exerted by each individual point charge.
The formula to calculate the electric force between two point charges is given by Coulomb's Law:
F = k * |q1| * |q2| / r^2
where:
F is the force between the charges,
k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the two charges.
In this case, we have three charges: q1 = 2 microC, q2 = -4 microC, and q3 = 7 microC.
Since the triangle is equilateral, the distances between all the charges are the same. Let's call this distance "d."
When calculating the resultant electric force on the 7 microC charge, we need to consider the forces exerted by the other two charges.
For the 7 microC charge and the 2 microC charge:
F1 = k * |q1| * |q3| / d^2
For the 7 microC charge and the -4 microC charge:
F2 = k * |q2| * |q3| / d^2
The resultant force, FR, can be calculated by adding the vectors of F1 and F2:
FR = F1 + F2
Substituting the values:
F1 = k * 2 * 7 / d^2,
F2 = k * 4 * 7 / d^2,
FR = F1 + F2.
Note: The direction of the forces will depend on the direction of the charges. Make sure to consider the signs and direction while adding the forces vectorially.
By substituting the appropriate values, you can now calculate the resultant force on the 7 microC charge.
so you have two forces, 120 degrees apart when added head to tail. Sketch the diagram (one force is attractive, one repulsive, add them head to tail.
Use law of cosines.