Question

Two point charges are brought closer together, increasing the force between them by a factor of 22. By what factor did their separation decrease? Hint: If the force increases, distance between charges must decrease. Force is indirectly proportional to the distance squared.

Answer 1

The separation between two point charges decreased by a factor of 5.

Step-by-step explanation:

To find the factor by which the separation between two point charges decreased when the force between them increased by a factor of 25, we need to understand the relationship between force and distance. According to Coulomb's law, the force between two point charges is inversely proportional to the square of the distance between them. This means that when the distance decreases, the force increases, and vice versa.

Since the force increased by a factor of 25, we can find the factor by which the distance decreased by taking the square root of 25, which is 5.

Therefore, the separation between the two point charges decreased by a factor of 5.

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Answer 2

Answer:0.21

Step-by-step explanation:

Given

Two point charges are brought closer together, increasing the force by a factor of 22

Let the original force be

`F=(kq_1q_2)/(r^2)---1`

where
`q_1,q_2` are charges and r is the distance between them

new force
`F'=(kq_1q_2)/(r'^2)----2`

divide 1 & 2

`(F')/(F)=((kq_1q_2)/(r'^2))/((kq_1q_2)/(r^2))`

`22=(r^2)/(r'^2)`

`r'=(r)/(√(22))\approx 0.213 r`

Distance between them is decrease by a factor of 0.21