Rate of change of potential difference if no magnetic field at distance 20 mm?

A physics teacher tries to build a device that illustrates Maxwell's generalization of Ampere's law. She drills a hole in the center of each plate of a parallel-plate capacitor and then runs a wire through the holes (Figure 1). There is no connection between the wire and the plates, and the potential difference across the plates can be controlled. In particular, what must be the rate of change of the potential difference if she wants no magnetic field at a distance r = 20 mm from the wire when it carries a steady current of 0.0200 A and the distance between the plates is d = 3.0 mm ?

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  • Anonymous
    9 months ago
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    We want the displacement current's magnetic field at r to be the same magnitude as the wire's magnetic field at r, but in the opposite direction (so the 2 fields will cancel).

    So the required displacement current through the area (radius r) must therefore be 0.0200A downwards.

    Displacement current: I_dis = ε₀dΦ/dt = ε₀ d(EA)/dt = ε₀A dE/dt

    Since E = V/d, dE/dt = (1/d)dV/dt

    I_dis = ε₀A (1/d) dV/dt

    dV/dt = d I_dis / (ε₀A)

    = 0.0030 * 0.0200 / (8.85*10-12 * π*0.02²)

    = 5.4x10^9 V/s

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