Question

4. By what factor will the electric force

between two charged objects change
if the distance between the objects is
quadrupled?
O 1/4
O 1/8
O 1/16
O 4

Answer 1

The factor by which the electric force between two charged objects change if the distance between the objects is quadrupled is
`(1)/(16)`.

Answer: Option C

Step-by-step 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

`\mathrm{F}=\frac{\mathrm{k} * \mathrm{q} * \mathrm{Q}}{\mathrm{d}^(2)}`

Now if the distance of separation is quadrupled then the modified force acting on them will be denoted as follows:

`F^(\prime)=(k * q * Q)/((4 d)^(2))=(k * q * Q)/(16 d^(2))=\left((1)/(16)\right) F`

So, the electric force will be reduced by a factor of
`(1)/(16)` when the distance of separation is quadrupled.