The drawing shows an equilateral triangle, each side of which has a length of 4.53 cm. Point charges are fixed to each corner, as shown. The 4.00 C charge experiences a net force due to the charges qA and qB. This net force points vertically downward and has a magnitude of 779 N. Determine (a) charge qA, (b) charge qB.
To determine the charges qA and qB, we can use Coulomb's Law, which states that the force between two charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Here's how you can calculate the charges qA and qB:
Step 1: Calculate the distance between the charges
Since we have an equilateral triangle, all sides are equal. Therefore, the distance between the 4.00 C charge and qA (or qB) can be calculated using the formula for an equilateral triangle:
distance = side length / (√3)
distance = 4.53 cm / (√3) ≈ 2.62 cm
Step 2: Calculate the force between the 4.00 C charge and qA (or qB)
Using Coulomb's Law:
force = k * (|charge1| * |charge2|) / distance^2
where k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2/C^2)
Given that the net force is 779 N, we need to consider the force as an algebraic quantity (with direction). Since the force points vertically downward, we assign a negative sign to the magnitude.
Therefore:
-779 N = -k * (4.00 C * qA) / (2.62 cm)^2
-779 N = -8.99 x 10^9 N m^2/C^2 * (4.00 C * qA) / (2.62 x 10^-2 m)^2
Step 3: Solve for qA (and similarly for qB)
Rearranging the equation, we can solve for qA:
qA = (√3 * distance^2 * magnitude of force) / (4.00 C * electrostatic constant)
Calculating qA:
qA = (√3 * (2.62 x 10^-2 m)^2 * (-779 N)) / (4.00 C * 8.99 x 10^9 N m^2/C^2)
After evaluating the expression, you can determine the values of qA and qB by substituting the distance, magnitude of the force, the charge of the 4.00 C charge, and the electrostatic constant into the equation.