Danger? I laugh at danger!

One day, I was out bicycling when a thunderstorm cropped up. While frantically pedaling home at a speed of \(10~\mbox{km/hr}\), a wind blew a power line down and it brushed against the inside of my front wheel, putting a positive \(1~\mbox{C}\) charge on the wheel. I kept pedaling. If my bicycle wheels have radius \(0.3~\mbox{m}\), what is the magnitude of the generated magnetic field in Teslas that I on my bike would measure at a distance of \(0.1~\mbox{m}\) perpendicular from the center of my front wheel?

Details and assumptions

  • Treat the wheels as thin conducting hoops.
  • You may assume the charge has spread out over the wheel but not left it yet.
  • My bike wheel was not slipping on the ground as I traveled.
  • The vacuum permeability is \(\mu_0=4\pi \times 10^{-7}~\mbox{H/m}\).

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