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Suppose a circular coil of radius 2.50 cm and containing 725 turns is in a magnetic field of 0.850 T. Initially the plane of the coil is perpendicular to the field but the coil is rotated through 360° in 0.520 seconds. If the resistance of the coil is 1.80 Ω, determine the energy required to rotate the coil through 90°

User Ghickman
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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.

Learn more about Electromagnetic Induction

User Jamie S
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