Respuesta :
Answer:
The new separation is [tex]\bf{(d/\sqrt{3})}[/tex].
Explanation:
The expression of the force between two spheres is given by
[tex]F = k\dfrac{q_{A}q_{B}}{d^{2}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)[/tex]
where, [tex]q_{A}[/tex] is the charge on sphere A, [tex]q_{B}[/tex] is the charge on sphere B, [tex]k[/tex] is constant and [tex]d[/tex] i the separation between two spheres.
The new value of charge on sphere B is [tex]q_{B}^{n} = \dfrac{q_{A}}{3}[/tex]. Consider the new separation between the spheres be [tex]d'[/tex]. Under the new configuration the force between the spheres is given by
[tex]F = k \dfrac{q_{A}(q_{A}/3)}{d'^{2}}~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)[/tex]
Equating equation (1) and equation (2), we have
[tex]~~~~&& \dfrac{1}{d'^{2}} = \dfrac{1}{3d^{2}}\\&or,& d' = \dfrac{d}{\sqrt{3}}[/tex]
So, the new separation is [tex](d/\sqrt{3})[/tex].
