charges of +1.000 C are located at the corners of a 45-45- right triangle which has a hypotenuse that is 1.414 m long. Determine the resultant force on the charge located at the vertex of the right angle.
The two charges at the 45 degree corners are each 1.0 m from the charge at the right angle.
There are two perpendicular forces acting on the right angle vertex charge. Each has magnitude
k Q^2/(1.0m^2)
where Q = 1.0C and k is the Coulomb constant. (look it up)
Add thse two forces as vectors. The magnitude should be sqrt2 * the magnitude of the individual forces. The direction will be along the bisector of the right angle.
To determine the resultant force on the charge located at the vertex of the right angle, we need to calculate the electric field due to each individual charge at that location, and then add up these electric fields vectorially to find the resultant electric field. Finally, we can use the electric field to calculate the resultant force using the formula F = qE, where F is the force, q is the charge, and E is the electric field.
Let's break it down step by step:
1. Calculate the electric field due to each charge:
- The distance from the charge to the vertex at the right angle is L = 1.414 m.
- The first charge at one of the corners has a charge of +1.000 C. The electric field at the vertex due to this charge is given by the formula E = k * q / r^2, where k is the Coulomb's constant (k = 9 * 10^9 N m^2/C^2), q is the charge (q = +1.000 C), and r is the distance from the charge to the vertex (r = L).
- Repeat the same calculation for the other two charges at the remaining corners.
2. Add up the electric fields:
- Since electric field is a vector quantity, we need to consider both the magnitude and direction of each electric field.
- Treat each electric field as a vector with an appropriate magnitude and direction (taking into account the positive or negative charge).
- Combine the three vectors using vector addition to obtain the resultant electric field.
3. Calculate the resultant force:
- Once we have the resultant electric field, we can calculate the resultant force by multiplying the charge at the vertex (+1.000 C) with the magnitude of the resultant electric field.
By following these steps, you should be able to determine the resultant force on the charge located at the vertex of the right angle.