Answer:
a. 0 Nm b. 1.30 × 10⁻²¹ Nm c. -1.30 × 10⁻²¹ Nm
Step-by-step explanation:
The magnitude of the torque τ on a dipole in a magnetic field is given by
τ = pEsinθ where p = qd = dipole moment and q = charges = 2e and d = distance between charges = 0.88 nm = 0.88 × 10⁻⁹ m, p = 2ed and E = electric field strength = 4.6 × 10⁶ N/C. θ = angle between E and p
a. When p and E are parallel, θ = 0°
τ = pEsinθ = τ = pEsin0 = pE × 0 = 0 Nm
b. When p and E are perpendicular, θ = 90°
τ = pEsinθ = τ = pEsin90 = pE × 1 = pE = 2edE = 2 × 1.602 × 10⁻¹⁹ C × 0.88 × 10⁻⁹ m × 4.6 × 10⁶ N/C = 12.97 × 10⁻²² Nm = 1.297 × 10⁻²¹ Nm ≅ 1.30 × 10⁻²¹ Nm
c. When p and E are antiparallel, θ = 180°
τ = pEsinθ = τ = pEsin180 = pE × -1 = pE = -2edE = -2 × 1.602 × 10⁻¹⁹ C × 0.88 × 10⁻⁹ m × 4.6 × 10⁶ N/C = -12.97 × 10⁻²² Nm = -1.297 × 10⁻²¹ Nm ≅ -1.30 × 10⁻²¹ Nm