In the figure Q=4.6 nC and all other quantities are exact. What is the magnitude of the force on the charge Q?
The figure is a triangle with equal sides of 1cm and 60 degree angles. Two of the corners on the bottom of the triangle has a charge of +2nC and Q is the top corner of the triangle.
To find the magnitude of the force on the charge Q, we can use Coulomb's law, which states that the magnitude of the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
In this case, the charge at the bottom corners of the triangle is +2 nC. Let's call one of these charges Q1 and the other Q2. Since the charges have the same magnitude and opposite signs, the net charge at each corner is 2 nC.
The distance between Q and each of the bottom corners can be found using trigonometry. Since the triangle has equal sides of 1 cm and 60-degree angles, we can use the sine function to determine the vertical distance between Q and the bottom corners.
The vertical distance from Q to the bottom corners is equal to half the height of an equilateral triangle, which can be found using the formula:
height = (side length * √3) / 2
Substituting the values, we get:
height = (1 cm * √3) / 2
Now, we can calculate the vertical distance between Q and the bottom corners by multiplying the height by the sine of 60 degrees:
vertical distance = (1 cm * √3) / 2 * sin(60°)
Next, we can calculate the force between Q and each of the charges at the bottom corners using Coulomb's law:
force = (k * |Q1 * Q|) / distance^2
Substituting the values, where k is Coulomb's constant (k ≈ 8.99 x 10^9 N m^2/C^2), Q1 = 2 nC, and distance is the vertical distance from Q to the bottom corners, we get:
force = (8.99 x 10^9 N m^2/C^2 * |2 nC * 4.6 nC|) / distance^2
Now, we can calculate the magnitude of the force on charge Q by summing the forces from each bottom corner:
total force = 2 * force
By plugging in the values and performing the calculation, you will get the magnitude of the force on the charge Q.