The velocity of each electron at the corners of the square is 15.92 m/s.
The given parameters;
- charge of electron, q = 1.6 x 10⁻¹⁹ C
- length of the square, L = 0.8 m
The diagonal length of the square is calculated as;
[tex]d^2 = 0.8^2 + 0.8^2\\\\d = \sqrt{0.8^2 + 0.8^2} \\\\d = 1.13 \ m[/tex]
The distance of each corner charge and the middle charge is calculated as;
[tex]r = \frac{1.13}{2} \\\\r = 0.565 \ m[/tex]
The force between each corner charge and the middle charge is calculated as;
[tex]F= \frac{kq^2}{r^2}[/tex]
The centripetal force on each charge moving around the square is calculated as;
[tex]F = \frac{mv^2}{r}[/tex]
solve the forces together;
[tex]\frac{mv^2}{r} = \frac{kq^2}{r} \\\\v^2 = \frac{kq^2}{m} \\\\v = \sqrt{ \frac{kq^2}{m} } \\\\v = \sqrt{ \frac{(9\times 10^9) \times (1.602\times 10^{-19})^2}{9.11 \times 10^{-31}} } \\\\v = 15.92 \ m/s[/tex]
Thus, the velocity of each electron at the corners of the square is 15.92 m/s.
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