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प्रश्न
Three-point charges +q, +2q and Q are placed at the three vertices of an equilateral triangle. Find the value of charge Q (in terms of q), so that the electric potential energy of the system is zero.
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उत्तर
Let ‘r’ be the side of the equilateral triangle,
`("U")_"AB" = 1/(4piε_0).("q".2"q")/"r"`
`("U")_"BC" = 1/(4piε_0).(2"q"."Q")/"r"`
`("U")_"AC" = 1/(4piε_0).("q"."Q")/"r"`
Since the electric potential energy of the system is zero.
∴ `("U")_"AB" + ("U")_"BC" + ("U")_"AC" = 0`
∴ `1/(4piε_0).(2"q"^2)/"r" + 1/(4piε_0).(2"q""Q")/"r" + 1/(4piε_0).("q""Q")/"r" = 0`
∴ 2q2 + 2qQ + qQ = 0
∴ 3qQ = -2q2
∴ Q = `(-2"q")/3`
∴ The value of charge Q (in terms of q) is `underline((-2"q")/3).`
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