An electric dipole consists of charges 2e and 2e separated by 0.88 nm It is in an electric field of strength 4.6 106 N C Calculate the magnitude of the torque on the dipole when the dipole moment is a parallel to b perpendicular to and c antiparallel to the electric field

a. 0 Nm b. 1.30 × 10⁻²¹ Nm c. -1.30 × 10⁻²¹ Nm

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

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