Respuesta :
The factor by which the electric force between two charged objects change if the distance between the objects is quadrupled is [tex]\frac{1}{16}[/tex].
Answer: Option C
Explanation:
Based on coulomb's law, the electric force acting between two charged objects separated by a distance is directly proportionate to the products of the charge of the objects and inversely proportionate to the distance squared between them. So if q and Q are two charges separated by a distance d than the electric force according to coulomb's law can be written as
[tex]\mathrm{F}=\frac{\mathrm{k} \times \mathrm{q} \times \mathrm{Q}}{\mathrm{d}^{2}}[/tex]
Now if the distance of separation is quadrupled then the modified force acting on them will be denoted as follows:
[tex]F^{\prime}=\frac{k \times q \times Q}{(4 d)^{2}}=\frac{k \times q \times Q}{16 d^{2}}=\left(\frac{1}{16}\right) F[/tex]
So, the electric force will be reduced by a factor of [tex]\frac{1}{16}[/tex] when the distance of separation is quadrupled.
