Question

Three point charges are arranged on a line. Charge q₃ = +5.00nC and is at the origin. Charge q₂ = -2.50 nC and is at x = 3.50 cm . Charge q₁ is at x = 1.50 cm

A). What is q₁ (magnitude and sign) if the net force on q₃ is zero?

Answer 1

A). To maintain a net force of zero on q₃, the charge q₁ must be +2.50 nC.

Step-by-step explanation:

In an equilibrium situation where the net force on q₃ is zero, the charges must be positioned such that the electrical forces cancel each other out.

Considering Coulomb's law, F = k * |q1 * q3| / r^2, where F is the force between charges q1 and q3, k is Coulomb's constant, q1 and q3 are the charges, and r is the distance between them. For a net force of zero on q₃, the forces between q₃ and q₁, as well as q₃ and q₂, must balance each other.

Given q₃ = +5.00nC at the origin and q₂ = -2.50 nC at x = 3.50 cm, the charge q₁ at x = 1.50 cm needs to be +2.50 nC for the forces on q₃ to cancel out.

This results in equal but opposite forces between q₃ and q₁, and q₃ and q₂, maintaining equilibrium on q₃. The negative charge q₂ and the positive charge q₁ create forces in opposite directions, ultimately balancing the net force on q₃.