Let's start by drawing a diagram of the overall setup. Place Q1 at the origin (0,0), Q2 right from Q1 along the x-axis, and q on top of the triangle above the origin. Let the distance between Q1 and q be a and between Q1 and Q2 be b.
We can use Coulomb's Law to find the magnitudes of the forces between the charges. The electric force between two charges is given by:
F = k * |q1 * q2| / r^2
where k is the electrostatic constant (approximately 8.99 * 10^9 N(m/C)^2), q1 and q2 are the magnitudes of the point charges, and r is the distance between them.
First, we'll find the magnitude of the force between Q1 and q:
F_Q1q = k * |Q1 * q| / a^2
Then, we'll find the magnitude of the force between Q2 and q:
F_Q2q = k * |Q2 * q| / b^2
Next, we'll find the horizontal and vertical components of these forces.
The force between Q1 and q has a horizontal component F_Q1qx and a vertical component F_Q1qy. The horizontal component is perpendicular to the right triangle and is given by:
F_Q1qx = F_Q1q
The vertical component points straight up and is given by:
F_Q1qy = 0
The force between Q2 and q has a horizontal component F_Q2qx and a vertical component F_Q2qy. The horizontal component is perpendicular to the right triangle and is given by:
F_Q2qx = F_Q2q * (b / sqrt(a^2 + b^2))
The vertical component points straight up and is given by:
F_Q2qy = F_Q2q * (a / sqrt(a^2 + b^2))
Now we can add the horizontal and vertical components to find the total force.
F_x = F_Q1qx - F_Q2qx = F_Q1q - F_Q2q * (b / sqrt(a^2 + b^2))
F_y = F_Q1qy + F_Q2qy = F_Q2q * (a / sqrt(a^2 + b^2))
Next, we'll find the magnitude and direction of the total force.
magnitude = sqrt(F_x^2 + F_y^2)
direction = arctan(F_y / F_x)
Plugging in the values for a, b, Q1, Q2, and q from the problem, we get:
F_Q1q = 8.99 * 10^9 * (0.83 * 10^(-6) * -0.63 * 10^(-6)) / a^2
F_Q2q = 8.99 * 10^9 * (0.9 * 10^(-6) * -0.63 * 10^(-6)) / b^2
magnitude = sqrt((F_Q1q - F_Q2q * (b / sqrt(a^2 + b^2)))^2 + (F_Q2q * (a / sqrt(a^2 + b^2)))^2)
direction = arctan(F_Q2q * (a / sqrt(a^2 + b^2)) / (F_Q1q - F_Q2q * (b / sqrt(a^2 + b^2))))
Note that the values for a and b are not given, so we cannot find the magnitude and direction of the total force numerically. However, you can plug in the known values for Q1, Q2, and q into these expressions to find the formulas for the magnitude and direction of the total force on q due to the other two charges.
Three point charges are fixed in place in a right triangle. What is the electric force on the q = -0.63 µC charge due to the other two charges? (Let Q1 = +0.83 µC and Q2 = +0.9 µC.)
what is the magnitude N, and direction in degrees ° above the positive x-axis?
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