Consider two long, cylindrical, concentric conductors whose cross-section is sho

Question

Consider two long, cylindrical, concentric conductors whose cross-section is shown in the figure. We will define the charge in these conductors in terms of the charge per unit of length along the axial direction (perpendicular to the page in the figure). Let lambda (lambda > 0) be the charge per unit length on the outer conductor, and let -lambda be the charge per unit length on the inner conductor. What is the direction of the electric field for r > b? A. Radially outward B. Radially inward C. The electric field in this region is zero. What is the direction of the electric field for a

Explanation / Answer

From Gauss law,

net flux through a concentric conductor of length = Qin/e0

E (2 pi r L ) = lambda L / e0

if net charge is negative then radially inward.

if Qin is positive then radially outward.

if Qin = 0 then E = 0

4. r > b, Qin = lambda + (-lambda) = 0

E = 0

Ans: (C)

5. a < r < b ; Qin > 0

then E is radially outward.

Ans: (A)

6. for r < a ; field inside conductor E = 0

Ans(C)

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