3 equal charges each of of 2*10-6 C are fixed at three corners of an equilateral triangle ofsides 5 cm.find the column force experienced by one of the charge due to the other two
To find the Coulomb force experienced by one of the charges due to the other two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges
k is the electrostatic constant, which is approximately equal to 9 × 10^9 N m^2/C^2
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, we have three charges of magnitude 2 * 10^(-6) C each fixed at the corners of an equilateral triangle. The side length of the triangle is 5 cm.
Since the triangle is equilateral, all three sides are equal. So, the distance between any two charges is 5 cm.
Now, let's calculate the Coulomb force experienced by one charge due to the other two charges:
First, substitute the given values into the formula:
F = (9 * 10^9 N m^2/C^2) * ((2 * 10^(-6) C)^2) / (0.05 m)^2
Simplifying this equation will give you the result which represents the force experienced by one of the charges due to the other two charges.
To find the electrostatic force experienced by one charge due to the other two charges, we can use Coulomb's law.
Coulomb's law states that the electrostatic force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:
F = k * (q1 * q2) / r^2
Where:
F is the electrostatic force
k is the electrostatic constant, approximately 9 x 10^9 Nm^2/C^2
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
In this case, since all three charges have the same magnitude of 2 * 10^-6 C and the triangle is equilateral, the distances between the charges will be the same. Let's call this distance 'd'.
Now, the force experienced by one charge due to the other two can be obtained by calculating the force between each pair of charges and adding them together since the charges are fixed and hence form a closed triangle.
Let's calculate the electrostatic force due to one pair of charges:
F1 = k * (q1 * q2) / d^2
F2 = k * (q2 * q3) / d^2
F3 = k * (q3 * q1) / d^2
Since all three charges are equal, we can rewrite these equations as:
F1 = F2 = F3 = k * (q^2) / d^2
Now, we can calculate the electrostatic force experienced by one charge due to the other two charges by adding the forces:
F_total = F1 + F2 + F3
= 3 * k * (q^2) / d^2
= 3 * (9 x 10^9 Nm^2/C^2) * (2 x 10^-6 C)^2 / (0.05 m)^2
Calculating this expression will give you the column force experienced by one of the charges due to the other two.