three point charges-1*10^-6,-2*10^-6,3*10^-6.one kept at corners of an equilateral triangle of side 1m.what is potential at centre
The distance from a corner of the triangle to the center is 1/4 the side length, or 0.25 m.
Add up -k*(-1 -2 +3)*10^-6/(0.25)
where k is the Coulomb constant. The sum is zero.
let the center of the triangle be (0,0) and let one vertex be at (1/√3,0). Then the other vertices are at vectors (1/√3,2π/3) and (1/√3,4π/3)
A good discussion of this kind of problem can be found at
http://www.answermenu.com/245/find-expression-electric-potential-the-center-the-triangle
I got the distance from the center to the corner wrong; it is (2/sqrt3)*(1/2) = 1/sqrt3 meters. Because the distance is the same for each corner, you add up the charges in the numerator to get the total potential. The answer is still zero.
To find the potential at the center of an equilateral triangle with three point charges at its corners, you can follow these steps:
Step 1: Determine the distances between the charges and the center of the equilateral triangle. Since the triangle is equilateral, all three distances are the same and equal to the length of one of its sides, which is 1m.
Step 2: Use Coulomb's law to calculate the individual potentials due to each charge. The potential due to a point charge can be determined using the formula:
V = k * q / r
where V is the potential, k is the electrostatic constant (9 x 10^9 N m^2/C^2), q is the charge, and r is the distance between the charge and the point at which we are measuring the potential.
For the given charges, the individual potentials are:
V1 = k * (-1 x 10^-6 C) / 1m
V2 = k * (-2 x 10^-6 C) / 1m
V3 = k * (3 x 10^-6 C) / 1m
Step 3: Calculate the total potential at the center of the equilateral triangle by summing up the potentials due to each charge.
V total = V1 + V2 + V3
Substituting the values of V1, V2, and V3, and calculating the sum will give you the potential at the center of the equilateral triangle.