Charges of +2.0𝞵C, +3.0𝞵C and -8.0𝞵C are placed at the vertices of an equilateral triangle of side 10cm. calculate the magnitude of the force acting on the -8.0𝞵C charge due to the other two charges.
To calculate the magnitude of the force acting on the -8.0𝞵C charge due to the other two charges, we can use Coulomb's Law.
Coulomb's Law states that the magnitude of the force between two point charges is given by the equation:
F = k * |q1 * q2| / r^2
where:
- F is the magnitude of the force between the charges,
- k is the electrostatic constant (9.0 x 10^9 N m^2/C^2),
- q1 and q2 are the magnitudes of the charges,
- r is the distance between the charges.
In this example, we have two charges (+2.0𝞵C and +3.0𝞵C) and one charge (-8.0𝞵C) forming an equilateral triangle. The side length of the triangle is given to be 10 cm.
To find the force on the -8.0𝞵C charge, we need to calculate the individual forces between this charge and the other two charges, and then find the resultant force.
Step 1: Calculate the force between the -8.0𝞵C charge and the +2.0𝞵C charge
Using Coulomb's Law:
F1 = k * |(-8.0𝞵C) * (+2.0𝞵C)| / r^2
= k * |-16.0𝞵C^2| / r^2
Step 2: Calculate the force between the -8.0𝞵C charge and the +3.0𝞵C charge
Using Coulomb's Law:
F2 = k * |(-8.0𝞵C) * (+3.0𝞵C)| / r^2
= k * |-24.0𝞵C^2| / r^2
Step 3: Find the resultant force
Since the triangle is equilateral, the distance between charges will be the length of any side of the triangle, which is given as 10 cm. So, r = 10 cm.
The resultant force is found by adding the individual forces together:
Resultant Force = F1 + F2
Finally, we can plug in the values and calculate the magnitude of the force acting on the -8.0𝞵C charge.
F vector = F1 vector + F2 vector
magnitude of F1 = k (8*10^-6)(3*101^-6)/ (0.1)^2 attracting
Magnitude of F2 = k (8*10^-6)(2*106-6) / (0.1)^2 attracting
third charge at origin
assume x in direction from third charge to second
then
Fx = F1 - F2 cos 60
Fy = F2 sin 60
magnitude = sqrt( Fx^2 + Fy^2)