Final answer:
When the angle θ is 90° between the force and displacement, the work done is zero as the force is perpendicular to the displacement and there is no energy transfer in the direction of the movement.
Step-by-step explanation:
When the angle θ is 90°, and the force is perpendicular to displacement, the formula for work (W) is defined as W = Fd cosθ, where F is the magnitude of the force applied, d is the displacement, and θ is the angle between the force and displacement vectors. However, for θ = 90°, the cosine of 90 degrees is zero (cos(90°) = 0), which implies that the work done (W) is also zero (W = Fd cos(90°) = Fd × 0 = 0).
Since work is zero when the force is perpendicular to the displacement, there is no transfer of energy in the direction of the displacement. Additionally, motion along an equipotential in an electric field must be perpendicular to that field since no work is done moving a charge along an equipotential. In this case, work is also zero because W = qEd cos θ = qEd cos 90° = 0, where q is the charge and E is the electric field vector.