Suppose the two people in the previous problem move toward each other. Calculate the magnitude of the electrical force of one on the other when their separation is reduced by a factor of 10.

Question

Suppose the two people in the previous problem move toward each other. Calculate the magnitude of the electrical force of one on the other when their separation is reduced by a factor of 10.

Answer 1

Hi Jenson,

Since I don't know what the previous problem was, let's just call the electrical force they previously felt as F₁ and their distance r.

According to Coloumb's Law: F_e = k q₁q₂ / r²

What stays the same regardless of how far away these two people are from one another? k is Coloumb's constant and, unless something weird is happening, the charges of the two people will remain the same.

So if F₁ = k q₁q₂ / r², how can we represent the force when they are a factor of 10 further away? Well that's the same as saying F₂ = k q₁q₂ / (r/10)². When we relate F₁ and F₂ we can see that the force is reduced by a factor of 100. That is, F₁ = 100*F₂

I hope that helps! Let me know if you have any other questions.