Question

The energy stored by any pair of positive charges is inversely proportional to the distance between them, and directly proportional to their charges. Three identical point charges start at the vertices of an equilateral triangle, and this configuration stores 15 Joules of energy. How much more energy, in Joules, would be stored if one of these charges was moved to the midpoint of the opposite side

Answer 1

Answer:

 U = 25 J

Explanation:

The energy in a set of charges is given by

          U = $k \sum \frac{q_i}{r_i}$

in this case we have three charges of equal magnitude

          q = q₁ = q₂ = q₃

with the configuration of an equilateral triangle all distances are worth

          d = a

          U = k ( $\frac{q_1q_2}{ r_1_2 } + \frac{q_1q_3}{r_1_3} + \frac{q_2q_3}{r_2_3}$ )

we substitute

           15 = k q² (3 / a)

            k q² /a = 5

For the second configuration a load is moved to the measured point of the other two

          d₁₃ = a

The distance to charge 2 that is at the midpoint of the other two is

          d₁₂ = d₂₃ = a / 2

           U = k (\frac{q_1q_2}{ r_1_2 } + \frac{q_1q_3}{r_1_3} + \frac{q_2q_3}{r_2_3})

            U = k q² (  $\frac{2}{a} + \frac{1}{a} + \frac{2}{a}$ )

            U = (kq² /a) 5

substituting

            U = 5 5

            U = 25 J