Induction and Energy Transfers — Question 1

Question 1

A constant-speed rod converts mechanical input entirely into Joule heat

A .250-m rod moves at 4.00 m/s on rails in a perpendicular .600-T field. The closed circuit resistance is 3.00 ohms. Neglect friction, inductance and all other losses.

1. Find emf, current and the external force needed to maintain speed.

2. Compare mechanical input power with resistor heating.

Question 1 - Solution

A constant-speed rod converts mechanical input entirely into Joule heat

(a) Method and calculation

$$\mathcal E=B\ell v=(.600)(.250)(4.00)=.600\,V,\quad i=\mathcal E/R=.200\,A.$$$$\boxed{F_{\mathrm{ext}}=iB\ell=.0300\,N}.$$

(b) Interpretation and further calculation

$$P_{\mathrm{ext}}=F_{\mathrm{ext}}v=(.0300)(4.00)=.120\,W.$$$$\boxed{P_R=i^2R=(.200)^2(3.00)=.120\,W}.$$

Physical check

The magnetic force brakes the rod, and the external agent supplies the dissipated energy.