Question

Is the new distance less than 10, equal to 10, or greater than 10 times the original distance?

Answer 1

The correct option is (1) less than 10 times the original distance.The original distance was  30 cm and the new distance is 94.86 cm which is less than 10 times the original.

What is Coulomb's force law?

The force of attraction and repulsion among two charged bodies are directly proportional to a product of their charges but inversely proportional to a square of a distance between them, according to Coulomb's law.

It works along the line that connects the two charges that are called point charges.

The formula for Coulomb's law is-

$f_{}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{}^{2}}$

where, q₁ and q₂ are the charges;

d is the distance between them.

Now, according to the question;

Two charges that were initially separated by a particular distance are pushed closer together until force between the two is reduced by a factor of ten.

Coulomb's law of force

$f_{1}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{1}{ }^{2}}$

d₁ is the initial distance.

So when charges are separated further, a new force is f₂, which is represented as

$f_{2}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}^{2}}$

d₂ is the moved distance

As a result, the given force is decreased by ten times its original value.

Thus, $f_{2}=\frac{f_{1}}{10}$

use the expression in both forces

$\begin{gathered} \frac{f_{1}}{10}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\\frac{q_{1} q_{2}}{4 \times 10 \pi \epsilon d_{1}{ }^{2}}=\frac{q_{1} q_{2}}{4 \pi \epsilon d_{2}{ }^{2}} \\ \frac{1}{10 \times d_{1}{ }^{2}}=\frac{1}{d_{2}{ }^{2}} \\ d_{2}=\sqrt{10} d_{1}\end{gathered}$

Now, calculate the moved distance d₂,

$\begin{aligned}& d_{2}=\sqrt{10} d_{1} \\ & d_{2}=\sqrt{10} \times 30 \\& d_{2}=3.162 \times 30 \\ & d_{2}=94.868 \mathrm{~cm}\end{aligned}$

The new distance is 94.868 cm.

Therefore, the new obtained distance is less than the 10 times the original distance.

To know more about the Coulomb's law of force, here

https://brainly.com/question/506926

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The complete question is-

Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10.  Is the new distance

(1) less than 10,

(2) equal to 10, or

(3) greater than 10;

times the original distance? If the original distance was 30 cm.