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Charges a and b in the figure are equal. each charge exerts a force on the other of magnitude
f. suppose the charge of b is increased by a factor of 4, but everything else is unchanged.

Respuesta :

MissPhiladelphia
The formula used to determine the force between two charges is
F = kQ1Q2/d2
The first has a and b with equal charges
F = k q q /d2
F = kq2/d2
In the second scenario, the charge of b is increased by 4
F = k q 4q /d2
F = 4kq2/d2
This means that increasing the charge by 4 also increases the force between  them by 4.
Eduard22sly

The new force of attraction between two charges will increase by a factor of 4

How to determine the initial force of attraction:

  • Initial charge of a (q₁) = 1 C
  • Initial charge of b (q₂) = 1 C
  • Electrical constant (K) = K
  • Distance apart (r) = r
  • Initial force (F₁) =?

F₁ = Kq₁q₂ / r²

F₁ = (K × 1 × 1) / r²

F₁ = K/r²

How to determine the new force

  • Final charge of a (q₁) = 1 C
  • Final charge of b (q₂) = 4 C
  • Electrical constant (K) = K
  • Distance apart (r) = r
  • Final force (F₂) =?

F₂ = Kq₁q₂ / r²

F₂ = (K × 1 × 4) / r²

F₂ = 4K/r²

Comparison of the force

  • Initial force (F₁) = K/r²
  • Final force (F₂) = 4K/r²
  • Comparison =?

F₂ / F₁ = 4K/r² ÷ K/r²

F₂ / F₁ = 4K/r² × r²/K

F₂ / F₁ = 4

F₂ = 4F₁

Thus, we can conclude that the new force will increase by a factor of 4

Learn more about Coulomb's law:

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