Generator for space station Astronauts on a space station...

Generator for space station Astronauts on a space station decide to use Earth's magnetic field to generate electric current. Earth's $\vec{B}$ field in this region has the magnitude of $3.0 \times 10^{-7} \mathrm{T}$ . They have a coil that rotates $90^{\circ}$ in 1.2 $\mathrm{s}$ . The area inside the coil measures 5000 $\mathrm{m}^{2}$ . Estimate the number of loops needed in the coil so that during that $90^{\circ}$ turn it produces an average induced emf of about 120 V. Indicate any assumptions you made. Is this a feasible way to produce electric energy?

Generator for space station Astronauts on a space station decide to use Earth's magnetic field to generate electric current. Earth's $\vec{B}$ field in this region has the magnitude of $3.0 \times 10^{-7} \mathrm{T}$ . They have a coil that rotates $90^{\circ}$ in 1.2 $\mathrm{s}$ . The area inside the coil measures 5000 $\mathrm{m}^{2}$ . Estimate the number of loops needed in the coil so that during that $90^{\circ}$ turn it produces an average induced emf of about 120 V. Indicate any assumptions you
made. Is this a feasible way to produce electric energy?

Key Concepts

Assumptions in Electromagnetic Generation

In analyzing electromagnetic induction scenarios, it is common to assume a uniform magnetic field over the area of the coil, a constant rotational speed when applicable, and idealized conditions such as negligible resistance and losses. These simplifications help focus on the underlying physics without the complexity introduced by real-world factors.

Coil Turns (Number of Loops)

Increasing the number of loops or turns in a coil directly increases the induced emf when the magnetic flux changes. Each loop contributes to the total voltage, making the design of coils a crucial factor in the efficiency and output of electromagnetic generators.

Feasibility of Energy Conversion Methods

Evaluating the feasibility of using electromagnetic induction for energy production involves considering the strength of the magnetic field, the rate of flux change, and practical factors such as the size of the coil and energy losses. Although the principles work in theory, the practical efficiency and output depend on the availability of sufficient changes in magnetic flux and manageable system losses.

Faraday's Law of Electromagnetic Induction

This principle explains that an electromotive force (emf) is induced in a circuit when there is a change in magnetic flux through the circuit over time. The induced emf is proportional to the rate of change of flux and the number of loops in the coil, forming the basis for most electrical generators.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is defined as the product of the magnetic field strength, the area it penetrates, and the cosine of the angle between the field direction and the normal to the area. A change in any of these factors can result in an induced voltage according to Faraday’s law.

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