Pls help me out.
Four positive and equal charges are located dt the corners of a square of side 20cm.if each charge has a magnitude 2microcoulumb,calculate the force acting on the charge at the lower left corner of the square.
Symettry makes the problem go away.
On the adjacent corners: F=kqq/s^2 * cos45
note that you resolve the force into two components, one component in the direction of the diagonal (above), and a perpendicular. However, the perpendicular to the normals from each corner cancel each other, as they are opposite directions. So you are left with the forces from corners in the direction of the normal
Fcorners=2*kqq/s^2 *cos45
now add the force from the diagonal charge.
Fdiag=kqq/(s*sqrt2)^2=1/2 kqq/s^2
add that to Fcorners, and you have it.
Make certain you understand this problem, you will see it again.
To calculate the force acting on the charge at the lower left corner of the square, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Given that each charge has a magnitude of 2 microcoulombs, and the side of the square is 20 cm, we know that the distance between any two charges on adjacent corners is 20 cm.
Let's label the charges A, B, C, and D, arranged in a square. The charge at the lower left corner is A. The charges at the other corners are B, C, and D.
To calculate the force on charge A, we need to calculate the forces between charge A and charges B, C, and D, and then add them up vectorially.
1. Calculate the forces between charge A and charges B, C, and D:
Force_AB = (k * Q_A * Q_B) / r^2
Force_AC = (k * Q_A * Q_C) / r^2
Force_AD = (k * Q_A * Q_D) / r^2
Where:
- k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
- Q_A, Q_B, Q_C, and Q_D are the magnitudes of the charges (2 microcoulombs)
- r is the distance between the charges (20 cm = 0.2 m)
2. Add up the forces vectorially:
Force_net = sqrt((Force_AB)^2 + (Force_AC)^2 + (Force_AD)^2)
Now let's plug in the values and calculate the force:
1. Calculate the forces:
Force_AB = (9 x 10^9 Nm^2/C^2 * (2 x 10^-6 C) * (2 x 10^-6 C)) / (0.2 m)^2
Force_AC = (9 x 10^9 Nm^2/C^2 * (2 x 10^-6 C) * (2 x 10^-6 C)) / (0.2 m)^2
Force_AD = (9 x 10^9 Nm^2/C^2 * (2 x 10^-6 C) * (2 x 10^-6 C)) / (0.2 m)^2
2. Add up the forces:
Force_net = sqrt((Force_AB)^2 + (Force_AC)^2 + (Force_AD)^2)
Calculating these values will give you the force acting on the charge at the lower left corner of the square.