Four equal point charge each of 16microcoulomb are placed on the four corners of a square of side 0.2m.calculate the force on any one of the charge
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To calculate the force on any one of the charges, we can use Coulomb's law, which describes the force between two point charges. The formula for Coulomb's law is as follows:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (approximately 9 * 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
In this case, the charges are all the same (16 microcoulombs) and the distance between them is the same (0.2m). Thus, we need to find the force on one charge due to three other charges.
Step 1: Calculate the force between one charge and one of the other charges:
F1 = k * (|q1| * |q2|) / r^2
Step 2: Since there are four charges, multiply the force calculated in Step 1 by 3 to get the total force on one charge due to the other three charges:
F_total = 3 * F1
Let's go ahead and calculate it.
Step 1:
F1 = (9 * 10^9 Nm^2/C^2) * (16 * 10^-6 C) * (16 * 10^-6 C) / (0.2m)^2
= (9 * 16 * 16 * 10^-6 * 10^-6 Nm^2/C^2) / (0.04m^2)
Calculating further, we get:
F1 = (2304 * 10^-12 Nm^2/C^2) / (0.04m^2)
= 57600 * 10^-12 Nm^2/C^2
Step 2:
F_total = 3 * (57600 * 10^-12 Nm^2/C^2)
= 172800 * 10^-12 Nm^2/C^2
= 1.728 * 10^-5 N
Hence, the force on any one of the charges is approximately 1.728 * 10^-5 Newtons.