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°]
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 charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
First, let's calculate the distance between the charges q2 and q3. Since the charges are fixed at the corners of an equilateral triangle, each side of the triangle will have a length of 3.70 cm. The distance between q2 and q3 is therefore equal to the length of one side of the equilateral triangle.
Next, we can calculate the electric force on q3 due to q1 and q2 separately, and then add them together to get the total electric force on q3.
Let's start by calculating the electric force between q1 and q3. The formula to calculate the electric force is:
F = (k * |q1 * q3|) / r^2
where F is the electric force, k is the electrostatic constant (approximately 9x10^9 N*m^2/C^2), |q1 * q3| is the product of the magnitudes of the charges q1 and q3, and r is the distance between them.
Substituting the given values into the formula, we have:
F1 = (9x10^9 * |+45.9nC * +91.8nC|) / (3.70cm)^2
Next, let's calculate the electric force between q2 and q3 using the same formula:
F2 = (9x10^9 * |+45.9nC * +91.8nC|) / (3.70cm)^2
Finally, we can add F1 and F2 together to get the total electric force on q3:
F_total = F1 + F2
By substituting the given values into the equations and performing the calculations, we can find the magnitude of the electric force on q3.