Question

Two charges q₁ and q₂ are placed 30cm apart, as shown in the figure. A third charge q₃ is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is [q₃/(4π∈0)]k, where is…. 

(A) 8q₂ 

(B) 8q₁ 

(C) 6q₂ 

(D) 6q₁

Answer 1

The correct option  (A) 8q₂

Explanation:

change in potential energy = final PE – initial PE

AC = 40 cm

AB = 30 cm

BC = 50 cm

∴ BD = 10 cm

initial PE = k[{(q₁q₃)/(AC)} + {(q₂q₃)/(BC)} + {(q₁q₂)/(AB)}]

Final PE = k[{(q₁q₃)/(AC)} + {(q₂q₃)/(BD)} + {(q₁q₂)/(AB)}]

∴ ΔPE = k[{(q₁q₃)/(AC)} + {(q₂q₃)/(BD)} + {(q₁q₂)/(AB)}  – {(q₁q₃)/(AC)} – {(q₂q₃)/(BC)} – {(q₁q₂)/(AB)}]

= k[{(q₂q₃)/(BD)} – {(q₂q₃)/(BC)}]

= kq₂q₃[(1/0.1) – (1/0.5)]

= kq₂q₃[10 – 2]

ΔPE = 8kq²q³ = [8/(4π∈₀)]q₂ q₃

given ΔPE = [q₃/(4π∈₀)]k

∴ [8/(4π∈₀)]q₂ q₃ = [q₃/(4π∈₀)]k

∴ 8q₂ = k