Two electrons are placed; one at north pole and other at south pole of earth. Find the force between them. Given diameter of earth= 12800 km.
(1.8)10to the power -24
To find the force between two electrons placed at the north pole and south pole of the Earth, we can use Coulomb's Law.
Coulomb's Law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula is given as:
F = (k * q1 * q2) / r^2
Where:
F = force between the two charges
k = Coulomb's constant (approximately 9 x 10^9 Nm^2/C^2)
q1, q2 = charges of the two electrons
r = distance between the charges
In this case, since both electrons have the same charge (negative), we can assign them the value of -1.6 x 10^-19 Coulombs.
The north pole and south pole are located at opposite ends of the Earth's diameter, so the distance between them is equal to the diameter of the Earth, which is 12800 km.
Converting the distance to meters, we have r = 12800 km = 12800 * 1000 m = 12,800,000 m.
Substituting the values into Coulomb's Law, we have:
F = (k * q1 * q2) / r^2
F = (9 x 10^9 Nm^2/C^2) * (-1.6 x 10^-19 C) * (-1.6 x 10^-19 C) / (12,800,000 m)^2
Calculating the expression, we get:
F = (9 x 10^9 Nm^2/C^2) * (2.56 x 10^-38 C^2) / (163,840,000,000 m^2)
F = 23.04 x 10^-29 N / 163,840,000,000,000,000 m^2
Simplifying further, we find:
F = 1.407 x 10^-46 N / m^2
Therefore, the force between the two electrons is approximately 1.407 x 10^-46 Newtons per square meter (N/m^2).
To find the force between two electrons placed at the North and South poles of the Earth, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's break down the problem step by step:
Step 1: Find the distance between the electrons.
The diameter of the Earth is given as 12,800 km.
Since one electron is at the North pole and the other is at the South pole, the distance between them is equal to the diameter of the Earth.
Distance between electrons = Diameter of Earth = 12,800 km = 12,800,000 meters (since 1 km = 1,000 meters)
Step 2: Calculate the force using Coulomb's Law.
Coulomb's Law equation is given as:
Force (F) = (k * |q1 * q2|) / r^2
Where:
F = Force between the charges
k = Coulomb's constant (k = 9 x 10^9 Nm^2/C^2)
q1, q2 = Charges of the two electrons
r = Distance between the electrons
Since we are dealing with electrons, both the charges (q1 and q2) will be equal, as the charge of an electron is considered unity.
q1 = q2 = e, where e is the charge of an electron = 1.6 x 10^(-19) C (coulombs)
Plugging in the values:
F = (9 x 10^9 Nm^2/C^2) * ((1.6 x 10^(-19) C) * (1.6 x 10^(-19) C)) / (12,800,000 m)^2
Now, let's calculate the force using a calculator:
F = (9 x 10^9) * ((1.6 x 10^(-19))^2) / (12,800,000)^2
F ≈ 0.095 N (approximately)
Therefore, the force between the two electrons placed at the North and South poles of the Earth is approximately 0.095 Newtons.
recall that the electric force
F = 9.0*10^9 (q1*q2)/r^2
So, plug in your values, remembering how many electrons are in a Coulomb, and you have only 1 electron at each pole. r must be in meters, of course, not km.