All Problems

Constant Magnetic Field, Magnetics

Problem 3.265

A parallel-plate capacitor with area of each plate equal to SS and the separation between them to dd is put into a stream of conducting liquid with resistivity ρ.\rho . The liquid moves parallel to the plates with a constant velocity v.v . The whole system is located in a uniform magnetic field of induction BB, vector B\mathbf{B} being parallel to the plates and perpendicular to the stream direction. The capacitor plates are interconnected by means of an external resistance RR. What amount of power is generated in that resistance? At what value of RR is the generated power the highest? What is this highest power eaual to?

Reveal Answer
 3.265. P=v2B2d2R/(R+ρd/S)2; when R=ρd/S, the power  is P=Pmax⁡=1/4v2B2dS/ρ\begin{aligned} &\text { 3.265. } P=v^{2} B^{2} d^{2} R /(R+\rho d / S)^{2} ; \text { when } R=\rho d / S, \text { the power }\\ &\text { is } P=P_{\max }=1 / 4 v^{2} B^{2} d S / \rho \end{aligned}
Prev
Next