Two small charges spheres are placed in vacuum on the x-axis: Q₁ = +3.0μC at the origin and Q₂ = -5.0μC at x = 40cm. Where must a third charge Q be placed if the force it experiences is to be zero?
To determine where the third charge Q must be placed so that the force it experiences is zero, we can use Coulomb's law. Coulomb's law states that the force between two charged objects is proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = k * (|Q₁| * |Q₂|) / r²
where F is the force, k is the electrostatic constant (k = 9.0 x 10⁹ N m²/C²), |Q₁| and |Q₂| are the magnitudes of the charges, and r is the distance between the charges.
In this case, we have two small charged spheres with charges Q₁ = +3.0μC and Q₂ = -5.0μC. We want to find the position where a third charge Q will experience zero force.
Since the force is zero, we can set up the following equation:
F = k * (|Q₁| * |Q|) / r₁² = 0
Since k and the magnitudes of Q₁ and Q are all non-zero constants, the only way for the equation to be satisfied is if r₁² (the distance between Q₁ and Q) approaches infinity, meaning that Q must be placed very far away from Q₁.
This means that the third charge Q should be placed at an extremely large distance from Q₁ in order for the force to be zero.