Figure ( a ) gives the magnitude E ( x ) of the electric fields that have been s
ID: 1323275 • Letter: F
Question
Figure (a) gives the magnitude E(x) of the electric fields that have been set up by a battery along a resistive rod of length L = 8.30 mm (see Figure (b)). The vertical scale is set by Es = 4.80 103 V/m. The rod consists of three sections of the same material but with different radii. (The schematic diagram of the figure (b) below does not indicate the different radii.) The radius of section 3 is 2.14 mm. What is the radius of (a) section 1 and (b) section 2?
Figure (a) gives the magnitude E(x) of the electric fields that have been set up by a battery along a resistive rod of length L = 8.30 mm (see Figure (b)). The vertical scale is set by Es = 4.80 ½103 V/m. The rod consists of three sections of the same material but with different radii. (The schematic diagram of the figure (b) below does not indicate the different radii.) The radius of section 3 is 2.14 mm. What is the radius of (a) section 1 and (b) section 2?Explanation / Answer
use the definition of resistivity (r) in terms of electric field (E) and current density (J) J = I/A, where A is the cross sectional area through which current I flows:
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
as figure is not visible,taken some of the values on my own
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