Question

In a system of n point charges electric potential at a point P having a distance r_i from the charge q_i is ________.

Options

• `1/(2piepsilon_0) sum "q"_"i"/"r"`

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

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

• `1/(4piepsilon_0) sum_1^"i" "q"_"i"/"r"_"i"`

Answer 1

In a system of n point charges electric potential at a point P having a distance r_i from the charge q_i is `underline(1/(4piepsilon_0) sum_1^"i" "q"_"i"/"r"_"i")`.

Explanation:

At a certain point, there is an electric potential. The labour required to get a unit positive charge from infinity to a point in an electric field is denoted by V. Because electric potential is a scalar quantity when there are many charges, the net potential will be the scaler sum of the potentials due to the individual charges.

`"V"_1 = "q"_1/(4piepsilon_0"r"_1); "V"_2 = "q"_2/(4piepsilon_0"r"_2); ... "V"_"i" = "q"_"i"/(4 pi epsilon_0 "r"_"i")`

And V = V₁ + V₂ + .... + V_i = `sum_1^"i" "q"_"i"/(4piepsilon_0"r"_"i") = 1/(4piepsilon_0) sum_0^"i" "q"_"i"/"r"_"i"`.