Magnetic Field in a capacitor
A parallel-plate capacitor with circular plates of radius 40 mm is being discharged by a current of 6.0 A. At what radius inside and outside the capacitor gap is the magnitude of the induced magnetic field equal to 75% of its maximum value?
Answer
A discharging parallel-plate capacitor creates a "displacement current" within the gap, which produces a magnetic field. You know the displacement current to be:
I_d = ε_0 dΦ/dt
where Φ is the electric flux. Use the equation for the electric field of a parallel plate capacitor and remember that current I = dQ/dt. From here you can find the flux and dΦ/dt to find the displacement current.
Now you can treat the displacement current like any other and use Ampere's law to find the magnetic field. (Draw an Amperian loop at some arbitrary radius)
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A discharging parallel-plate capacitor creates a "displacement current" within the gap, which produces a magnetic field. You know the displacement current to be:
I_d = ε_0 dΦ/dt
where Φ is the electric flux. Use the equation for the electric field of a parallel plate capacitor and remember that current I = dQ/dt. From here you can find the flux and dΦ/dt to find the displacement current.
Now you can treat the displacement current like any other and use Ampere's law to find the magnetic field. (Draw an Amperian loop at some arbitrary radius)