Part (a) of the figure below gives the magnitude E(x) of the electric fields tha

Question

Part (a) of the figure below gives the magnitude E(x) of the electric fields that have been set up by a battery along a resistive rod of length 9.00 mm (part (b) of the figure). The vertical scale is set by Es = 5.20 103 V/m. The rod consists of three sections of the same material but with different radii. (The schematic diagram of part (b) of the figure does not indicate the different radii.) The radius of section 3 is 5.60 mm.

(a) What is the radius of section 1?
mm

(b) What is the radius of section 2?
mm

Explanation / Answer

help: r = E/J Since all three sections of the rod are of the same material, r is the same for each section. Section 1: r = Es*5*A1/(8 *I) Section 2: r = Es*A2/I giving .. A2/A1 = 5/8 R2/R1 = squrt(5/8) R2 = 0.79*R1 = 1.63mm Section 3: r = Es*3*A3/(8 *I) = Es*5*A1/(8 *I) A3/A1 = 5/3 R3/R1 = squrt(5/3) R3 = 2.11mm

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