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

Question

Figure (a) 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 (figure (b)). The vertical scale is set by Es = 7.60 103 V/m. The rod consists of three sections of the same material but with different radii. (The schematic diagram of figure (b) does not indicate the different radii.) The radius of section 3 is 3.20 mm.

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

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

Explanation / Answer

To answer this question you can 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)----------------1

Section 3: r = Es*3*A3/(8 *I) = Es*5*A1/(8 *I)

A3/A1 = 5/3

R3/R1 = squrt(5/3)

R1 = 2.478 mm

substitute this value in equation 1

R2/R1 = squrt(5/8)

R2 =2.487*squrt(5/8)   = 1.96 mm

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.