Three charges, q1=+45.9nC q2=+45.9nC and q3=+91.8nC are fixed at the corners of an equilateral triangle with a side length of 3.70cm. Find the magnitude of the electric force on q3.
k =9•10^9 N•m²/C²
r=0.037m
F13=k•q1•q3/r²,
F23=k•q2•q3/r²,
Cosine law for forces:
F=sqrt[F13²+F23²- 2•F13•23•cos120°]
Elena, why do you have a 13 & 23 beside F? Or is this just to distinguish between the two forces
To find the magnitude of the electric force on q3, we can use Coulomb's Law. Coulomb's Law states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The equation for Coulomb's Law is:
F = k * |q1 * q2| / r^2
Where F is the magnitude of the electric force, k is the electrostatic constant (9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, we have three charges q1=+45.9nC, q2=+45.9nC, and q3=+91.8nC.
The distance between the charges is the side length of the equilateral triangle, which is given as 3.70cm.
Let's calculate the electric force on q3:
1. Convert the side length of the triangle to meters: 3.70cm = 0.0370m
2. Substitute the values into the Coulomb's Law equation:
F = (9.0 x 10^9 N m^2/C^2) * |(45.9nC) * (91.8nC)| / (0.0370m)^2
3. Simplify the equation:
F = (9.0 x 10^9 N m^2/C^2) * (45.9nC * 91.8nC) / (0.0370m)^2
Calculating the math results in the magnitude of the electric force on q3.