What Produces a Magnetic Field? — Question 8

Question 8

A revolving charged ring acts as a conventional current source

A thin insulating ring carries uniformly distributed charge Q=4.00 nanocoulomb and rotates at frequency f=200 revolutions per second. A fixed sensor has calibrated signed response B=kappa I for current around this ring, with kappa=.150 tesla per ampere.

1. Find the equivalent conventional current and sensor field.

2. If the charge is replaced by -Q while the mechanical rotation is unchanged, find the new current and field.

Question 8 - Solution

A revolving charged ring acts as a conventional current source

(a) Method and calculation

$$T=1/f,\quad I=Q/T=Qf=(4.00\times10^{-9})(200)=.800\,\mathrm{\mu A}.$$$$B=\kappa I=(.150)(.800\times10^{-6})=.120\,\mathrm{\mu T}.$$

(b) Interpretation and further calculation

$$I\prime=(-Q)f=-.800\,\mathrm{\mu A}.$$$$B\prime=\kappa I\prime=-.120\,\mathrm{\mu T}.$$

Physical check

Conventional current follows positive charge motion and opposes negative charge motion.