Consider a conductor in the shape of spherical shell with inner radius a and outer radius b. The current I is fed into the conductor at the inner surface with radius r = a. The current then flows within the conductor with a spherically symmetric flow in the radially outward direction. In other words, the current density within the conductor is J = Jf where the radial component J depends only on the radial coordinate r. The current is then collected at the outer surface at radius r= b. Let p be the resistivity of the conductor. You are going to compute the resistance Rof the conductor after a few steps. (a) Find the radial component of the current density, J, for a point within the conductor that has radial coordinate r (within the conductor means a
Consider a conductor in the shape of spherical shell with inner radius a and outer radius b. The current I is fed into the conductor at the inner surface with radius r = a. The current then flows within the conductor with a spherically symmetric flow in the radially outward direction. In other words, the current density within the conductor is J = Jf where the radial component J depends only on the radial coordinate r. The current is then collected at the outer surface at radius r= b. Let p be the resistivity of the conductor. You are going to compute the resistance Rof the conductor after a few steps. (a) Find the radial component of the current density, J, for a point within the conductor that has radial coordinate r (within the conductor means a
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Transcribed Image Text:Consider a conductor in the shape of spherical shell with inner radius a and outer radius b. The current I is fed into the conductor at the inner surface with radius r = a. The current then flows
within the conductor with a spherically symmetric flow in the radially outward direction. In other words, the current density within the conductor is J
depends only on the radial coordinate r. The current is then collected at the outer surface at radius r = b. Let p be the resistivity of the conductor. You are going to compute the resistance R of
= Jf where the radial component J
the conductor after a few steps.
(a) Find the radial component of the current density, J, for a point within the conductor that has radial coordinate r (within the conductor means a <r< b).
(b) Let E denote the radial component of the electric field. Find E as a function ofr.
E
(c) Find the potential difference, V=V(a) – V(b), between the inner and the outer surfaces of the conductor.
V =
(d) What is the resistance R of the spherical conductor?
R =
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