The distance between the charge and the source of the electric field is 2.2 m.
The potential energy U of a charge q placed in an electric field created by a source charge Q, at a distance r from the source charge is given by,
[tex] U=\frac{kQq}{r} [/tex] ...... (1)
Here, k is the Coulomb constant.
The electric field E at a distance r from the source charge is given by,
[tex] E =\frac{kQ}{r^2} [/tex] ......(2)
From equations (1) and (2)
[tex] U=E*q*r [/tex]
Rewrite the expression for ri.
[tex] r=\frac{U}{Eq} [/tex]
Substitute 75 J for U, [tex] 4.5*10^5 V/m [/tex] for E and [tex] 7.5*10^{-5} C [/tex] for q.
[tex] r=\frac{U}{Eq} \\ =\frac{75 J}{(4.8*10^{5} V/m)(7.2*10^{-5}C)} \\ =2.17 m [/tex]
Rounding off to the nearest tenth, the the distance between the charge and the source charge is 2.2 m
