To determine the change in potential energy of the system when moving charge q₃ along the arc from point C to point D, we can use the formula for electric potential energy between point charges. The potential energy change is influenced by the distances between the charges and their magnitudes.
Understanding the Setup
Given that q₁ and q₂ are separated by 30 cm, and q₃ moves along a circular path of radius 40 cm, we need to analyze how the potential energy changes as q₃ moves in relation to q₁ and q₂.
Potential Energy Formula
The potential energy (U) between two point charges is given by:
U = k * (q₁ * q₂) / r
where:
- k is Coulomb's constant (1/(4πε₀))
- r is the distance between the charges
Calculating the Change
As q₃ moves from C to D, the distances to q₁ and q₂ will change, affecting the potential energy. The problem states that the change in potential energy can be expressed as:
ΔU = (q₃)/(4πε₀) * k
Identifying the Correct Option
To find the correct answer among the choices provided (A: 8q₂, B: 8q₁, C: 6q₂, D: 6q₁), we need to consider the contributions from both q₁ and q₂ as q₃ moves along the arc.
After analyzing the distances and the contributions from both charges, the correct answer is:
A: 8q₂
