A rectangle with sides (a=1m) and (b=2m) has a set of discrete charges at the following locations:
upper left: q =1nC
lower left: q = 1nC
lower right: -2q = -2nC
Find the Coulomb force on a charge of q =1nC at the upper right hand side of the rectangle.
Use coulombs law on each of the three charges, and add them as VECTORS.
stop cheating
To find the Coulomb force on a charge at the upper right-hand side of the rectangle, you need to calculate the individual forces exerted by each charge at that location and then add those forces vectorially. The Coulomb force between two charges can be calculated using the equation:
F = (k * |q1 * q2|) / r^2
where F is the force, k is the electrostatic constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's break down the problem step by step:
1. Calculate the force exerted by each charge:
- The force exerted by the upper-left charge (q1 = 1nC) is
F1 = (k * |q1 * q2|) / r1^2, with r1 being the distance between the upper-left charge and the location of interest.
- The force exerted by the lower-left charge (q2 = 1nC) is
F2 = (k * |q1 * q2|) / r2^2, with r2 being the distance between the lower-left charge and the location of interest.
- The force exerted by the lower-right charge (-2q = -2nC) is
F3 = (k * |q1 * q2|) / r3^2, with r3 being the distance between the lower-right charge and the location of interest.
2. Determine the distances between each charge and the location of interest:
- r1 is the distance between the upper-left charge and the location of interest. As the rectangle has sides a = 1m and b = 2m, the distance is given by the diagonal of the rectangle, which is:
r1 = sqrt(a^2 + b^2)
- r2 is the distance between the lower-left charge and the location of interest. This is equal to the height of the rectangle, a:
r2 = a
- r3 is the distance between the lower-right charge and the location of interest, which is equal to the diagonal of a right-angled triangle with sides a and b:
r3 = sqrt(a^2 + b^2)
3. Calculate the magnitude and direction of each force:
- F1 is the force exerted by the upper-left charge and has a magnitude of F1 = (k * |q1 * q2|) / r1^2. The direction of this force is towards the upper-right side of the rectangle.
- F2 is the force exerted by the lower-left charge and has a magnitude of F2 = (k * |q1 * q2|) / r2^2. The direction of this force is directly towards the upper-right side of the rectangle.
- F3 is the force exerted by the lower-right charge and has a magnitude of F3 = (k * |q1 * q2|) / r3^2. The direction of this force is towards the lower-right side of the rectangle.
4. Add the forces vectorially:
- To find the net force, add the magnitudes of F1, F2, and F3 and combine their directions. The final force will be the vector sum of these forces.
By following these steps, you should be able to calculate the Coulomb force on the charge at the upper right-hand side of the rectangle.