Faraday’s Homopolar Generator

Consider a perfectly conducting disk of radius r₀ in a constant magnetic field B perpendicular to the plane of the disk. Sliding contacts are provided

Figure 1.1

at the edge of the disk (C₁) and at its axle (C₂) (see Figure 1.1). This system is Faraday’s “homopolar generator.” When turned at constant angular velocity, it provides a large direct current with no ripple. A torque is produced by a mass M hung on a long string wrapped around the perimeter of the disk.

a) Explain how and why a current flows. Give a quantitative expression for the current as a function of angular velocity.

b) Given a long enough string, this system will reach a constant angular velocity ω_f . Find this ω_f and the associated current.

SOLUTION

a) Consider an electron at a distance r from the axle (see Figure 1.2). It experiences a Lorentz force

(1)

with v = ω × r, so we have a radial force F_r acting on the electron:

(2)

where is the electron charge. Therefore, the equivalent electric field E = -(1/c)ωRr, and the voltage between C₂ and C₁ is

The current i through the resistor R is given by

(3)

Figure 1.2

b) The power P dissipated in the resistance can be found from (3)

The kinetic energy of the disk

(4)

where I is the moment of inertia of the disk. From energy conservation, we may write

(5)

For a constant angular velocity  we have

(6)

So

(7)

and

(8)

مواضيع ذات صلة

مصطلحات الفيزياء النووية

إزاحة حمراء REDSHIFT

المركبات النانوية (Nanocomposites)

مولد فان دي جراف الالكتروستاتي

التطويرات التقنية الحديثة في المعجلات الالكتروستاتية

معجلات الالكترونات الالكتروستاتية

معجلات الفان دي جراف الترادفية

الحد من زيادة الطاقة في معجل فان دي جراف

أنبوبة التعجيل قي معجلات الجسيمات من نوع فان دي جراف

ارتكاز معجل فان دي جراف

مبدأ تشغيل معجل الفان دي جراف

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