A positive charge q₁ = 1.00 μC is fixed at the origin, and a second charge q2=-2.00 μC is fixed at x = 10.0 cm. Where along the x-axis should a third charge be positioned so that it experiences no force?

Answer 1

To find the position along the x-axis where a third charge experiences no force, we can use Coulomb's Law:

F = k * q₁ * q₂ / r²

Here, F is the force between q₁ and q₂, k is the electrostatic constant (9.0 x 10^9 N m²/C²), q₁ is the charge at the origin (1.00 μC = 1.00 x 10^-6 C), q₂ is the charge at x = 10.0 cm (-2.00 μC = -2.00 x 10^-6 C), and r is the distance between q₁ and q₂.

Since we want the third charge to experience no force, the force between the third charge and q₂ should be zero:

F = k * q₂ * q₃ / (10.0 cm - x)² = 0

We can solve this equation to find the value of x for which the force is zero:

k * q₂ * q₃ / (10.0 cm - x)² = 0

q₂ * q₃ / (10.0 cm - x)² = 0

Since the product q₂ * q₃ cannot be zero (as q₂ = -2.00 μC and q₃ is unknown), the denominator (10.0 cm - x)² must be zero. This occurs when x = 10.0 cm.

Therefore, the third charge should be positioned at x = 10.0 cm along the x-axis in order to experience no force.