Twelve charges of charge q are situated at the corners of the 12 sided polygon of side a.What is the net force on the charge Q at the centre
Question
Twelve charges of charge q are situated at the corners of the 12 sided polygon of side a.What is the net force on the charge Q at the centre
Solution
The net force on the charge Q at the center of the 12-sided polygon (dodecagon) due to the twelve charges q at the corners can be calculated using Coulomb's Law.
Step 1: Calculate the force between Q and one of the charges q.
Coulomb's Law states that the force between two charges is given by F = k*|q1*q2|/r^2, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.
In this case, q1 = Q, q2 = q, and r = a (the distance from the center of the polygon to a corner). So, the force between Q and one of the charges q is F = k*|Q*q|/a^2.
Step 2: Calculate the net force on Q due to all twelve charges.
Since the charges are symmetrically distributed around the polygon, the forces on Q due to each charge will cancel out in the horizontal and vertical directions. Therefore, the net force on Q is zero.
So, regardless of the values of Q, q, and a, the net force on the charge Q at the center of the 12-sided polygon is zero.
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