Answer:
636.4 J
Explanation:
The potential energy between one of the charges at the corner of the square and the fifth identical charge is U = kq²/r where q = charge = +50 × 10⁻⁶ C and r = distance from center of square. = √2 m (since the midpoint of the sides = 1 m, so the distance from the charge at the corner to the center is thus √(1² + 1²) = √2)
Since we have four charges, the additional potential energy to move the charge to the centre of the square is U' = 4U = 4kq²/r
U' = 4kq²/r
= 4 × 9 × 10⁹ Nm²/C² (+50 × 10⁻⁶ C)²/√2 m
= 900 Nm²/√2 m
= 636.4 J
The total external energy required is 636.4 J.
According to the question, a square of side a = 2m has 4 identical charges on the corners with charge Q = 50×10⁻⁶C.
A fifth identical charge is brought at the geometric center of the square. The geometric center is at the center of the diagonal:
[tex]r=\frac{a}{\sqrt{2} }=\sqrt{2}\;m[/tex]
The potential energy is a state function which means that it depends on the initial and final position.
Now the energy required is equal to the change in potential energy
[tex]\Delta U=\frac{1}{4\pi\epsilon_o}\frac{4Q^2}{r}\\\\\Delta U=\frac{4\times9\times10^9\times(50\times10^{-6})^2}{\sqrt{2} } \\\\\Delta U=636.4\;J[/tex]
Learn more about electric potential energy:
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