Question

If a charge q₀ is there in an electric field caused by several point charges q_i. The potential energy of q₀ is given by ________.

Options

• `1/(4piepsilon_0) sum("q"_"i""q"_0)/"r"`

• `1/(4piepsilon_0) sum("q"_"i""q"_0)/"r"^2`

• `1/(4piepsilon_0) sum("q"_"i""q"_0)/"r"^3`

• `1/(2piepsilon_0) sum("q"_"i""q"_0)/"r"`

Answer 1

If a charge q₀ is there in an electric field caused by several point charges q_i. The potential energy of q₀ is given by `underline(1/(4piepsilon_0) sum("q"_"i""q"_0)/"r")`.

Explanation:

Potential energy of charge q₀ placed at a distance r₁ in a field created by a single charge q₁ is `"U"_1 = ("q"_1"q"_0)/(4piepsilon_0"r"_1)`

In a field created by multiple charges q₁, q₂, q₃,…q_i, the potential energy of the charge q₀ is the scalar sum of potential energies due to each of the charges q₁, q₂, q₃,…q_i. As electrostatic potential energy is a scalar quantity. Thus, the total potential energy of the charge q₀ is U = `sum_1^"i" ("q"_"i""q"_0)/(4piepsilon_0"r"_"i") = 1/(4piepsilon_0) sum("q"_"i""q"_0)/"r"`.