Question

Consider the situation of the previous problem. A charge of −2.0 × 10⁻⁴ C is moved from point A to point B. Find the change in electrical potential energy U_B − U_A for the cases (a), (b) and (c). 

Answer 1

Given:
Magnitude of charge, q =  −2.0 × 10⁻⁴ C

(a) The electric field is along the x direction.
Thus, potential difference between (0, 0) and (4, 2),
dV = −E.dx = −20 × 4 = −80 V
Potential energy (U_B − U_A) between the points = dV × q 
⇒ U_B − U_A = (−80) × (−2.0 × 10⁻⁴)
⇒ U_B − U_A = 160 × 10⁻⁴ = 0.016 J

(b) A = (4 m, 2m), B = (6 m, 5 m)
dV = −E.dx = − 20 × 2 = −40 V
Potential energy (U_B − U_A) between the points = dV × q
⇒ U_B − U_A = (−40) × (−2 × 10⁻⁴)
⇒ U_B − U_A = 80 × 10⁻⁴ = 0.008 J

(c) A = (0, 0) B = (6m, 5m)
dV = −E.dx = −20 × 6 = −120 V
Potential energy (U_B − U_A) between the points A and B = dV × q
⇒ U_B − U_A = (−120) × (−2 × 10⁻⁴)
⇒ U_B − U_A = 240 × 10⁻⁴ = 0.024 J