Question

three point charges are arranged on a line. charge q3 = 5.00 nc and is at the origin. charge q2 = -4.00 nc and is at x = 3.50 cm . charge q1 is at x = 2.50 cm .What is q1 (magnitude and sign) if the net force on q3 is zero?

Answer 1

To find the magnitude and sign of charge q₁, we need to determine the position of q₁ relative to q₂ and q₃. By setting the forces between q₃ and q₁ equal to the forces between q₃ and q₂, we can solve for the magnitude and sign of q₁.

Step-by-step explanation:

To find the magnitude and sign of charge q₁, we need to first determine the position of q1 relative to q2 and q3. Since the net force on q3 is zero, the forces caused by q1 and q2 must balance each other out. Using Coulomb's Law, we can calculate the forces between q3 and q1 and q3 and q2. By setting these forces equal to each other and solving for q₁, we can find its magnitude and sign.

Let's assume the distance between q1 and q3 is d. The force between q3 and q1 is given by:

F₁₃ = (k * |q3| * |q₁|) / d²

The force between q3 and q2 is given by:

F₂₃ = (k * |q3| * |q₂|) / (d - 3.5 cm)²

Since F₁₃ is equal to F₂₃, we have:

(k * |q3| * |q₁|) / d² = (k * |q3| * |q₂|) / (d - 3.5 cm)²

Simplifying the equation, we can find q₁ in terms of q₂ and d:

q₁ = (|q₂| * (d - 3.5 cm)²) / d²