Figure ( a ) gives the magnitude E ( x ) of the electric fields that have been s

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 = 5.60 ×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 2.16 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 = 5.60 ×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 2.16 mm. What is the radius of (a) section 1 and (b) section 2 Es x=0 3 6 9 x(mm

Explanation / Answer

Es = 5.6 *10^3 V/m

r3 = 2.16 mm

a) for the radius of section 1 r1

as J = E * sigma

I/area = E * sigma

I/sigma = E * area

Now , for the section 1

(3/8) * Es * pi * r3^2 = (5/8) * Es * pi * r1^2

3 * 2.16^2 = 5 * r1^2

solving for r1

r1 = 1.67 mm

the radius of section 1 is 1.67 mm

b) for the section 2

(3/8) * Es * pi * r3^2 = Es * pi * r2^2

3 * 2.16^2 = 8 * r2^2

r2 =1.322 mm

the radius of section 2 is 1.322 mm

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