Question

In the rectangle, shown below, the two corners have charges q₁ = – 5μc and q₂ = + 2.0μc. The work done in moving a charge 3μc from B to A is [taken [1/(4π∈₀) = 1010 Nm²/c²]. 

(A) 5.5 J 

(B) 2.5 J 

(C) 3.5 J 

(D) 4.5 J

Answer 1

The correct option (B) 2.5 J

Explanation:

Potential B = V_B = k[q₁/(0.05)] + k[q₂/(0.15)]

= 9 × 10⁹[{(– 5 × 10^–6)/(0.05)} + {(2 × 10^–6)/(0.15)}]

= 9 × 10⁹ × 10^–6[(260)/3]

= – 7.8 × 10⁵ V

Potential at A,  V_A  = [(kq₁)/(0.15)] + [(kq₂)/(0.05)]

= k[{(– 5 × 10^–6)/(0.15)} + {(2 × 10^–6)/(0.05)}]

= 9 × 10⁹ × 10^–4 [{(– 1) / 3} + (2/5)]

= 0.6 × 10⁵ V

Work done in moving charge 3μc from B to A = 3 × 10^–6(V_A – V_B)

= 3 × 10^–6 × [0.6 × 10⁵ + 7.8 × 10⁵]

= 3 × 10^–6 × 10⁵[8.4]

= 25 × 2 × 10^–1

 = 2.52J