Question

In the diagram, q₁, q2, and q3 are in a straight line. Each of these particles has a charge of -2.35 x 10-⁶ C. Particles q₁ and q2 are separated by 0.100 m and particles q2 and q3 are separated by 0.100 m. What is the net force on particle q₁?​

ANSWERED: -6.21 N

Answer 1

To calculate the net force on particle q₁, we can use Coulomb's law to find the magnitude of the force between q₁ and q₂, as well as the force between q₁ and q₃. The force between two charges is given by:

F = k * (q₁ * q₂) / r²

where k is Coulomb's constant, q₁ and q₂ are the charges, and r is the distance between the charges.

Using this formula, we can find that the magnitude of the force between q₁ and q₂ is:

F₁₂ = k * (q₁ * q₂) / r₁₂² = (9 x 10⁹ N m²/C²) * ((-2.35 x 10⁻⁶ C)² / (0.100 m)²) = 5.54 x 10⁻⁴ N

Similarly, the magnitude of the force between q₁ and q₃ is:

F₁₃ = k * (q₁ * q₃) / r₁₃² = (9 x 10⁹ N m²/C²) * ((-2.35 x 10⁻⁶ C)² / (0.100 m)²) = 5.54 x 10⁻⁴ N

Since the charges q₂ and q₃ are equal in magnitude and opposite in sign, they will produce equal and opposite forces on q₁, which cancel each other out. Therefore, the net force on q₁ is:

F_net = F₁₂ + F₁₃ = (5.54 x 10⁻⁴ N) + (5.54 x 10⁻⁴ N) = 1.11 x 10⁻³ N

The direction of this force will be towards q₂, since the force between q₁ and q₂ is attractive. Therefore, the correct answer to the question is that the net force on particle q₁ is -1.11 x 10⁻³ N.