Final answer:
The energy required to rotate a circular coil in a magnetic field through any angle, including 90°, is zero, as the change in magnetic flux is zero, resulting in a zero induced emf.
Step-by-step explanation:
To determine the energy required to rotate the coil through 90°, we first need to determine the change in magnetic flux linked with the coil when it is rotated through 360°, and then calculate the energy for a 90° rotation.
The magnetic flux through the coil when the plane of the coil is perpendicular to the magnetic field is given by the equation Φ = BAN cosθ. Here, B is the magnetic field, A is the area of the coil, N is the number of turns in the coil, and θ is the angle between the plane of the coil and the direction of the magnetic field. Since the coil is rotated through 360°, the change in magnetic flux ΔΦ is zero.
According to Faraday's law of electromagnetic induction, the induced emf in the coil is given by ε = -N(ΔΦ/Δt), where Δt is the time interval. Since ΔΦ is zero, the induced emf ε is also zero. Therefore, no electrical energy is used when the coil is rotated.
The energy required to rotate the coil through 90° should be the same, i.e., zero, since the change in magnetic flux linked with the coil is also zero for a 90° rotation.
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