An infinite conducting cylindrical shell of outer radius r1 = 0.10 m and inner radius r2 = 0.08 m initially carries a surface ch
arge density σ = -0.35 μC/m2. A thin wire, with linear charge density λ = 1.1 μC/m, is inserted along the shells' axis. The shell and the wire do not touch and these is no charge exchanged between them.a) What is the new surface charge density, in microcoulombs per square meter, on the inner surface of the cylindrical shell?b) What is the new surface charge density, in microcoulombs per square meter, on the outer surface of the cylindrical shell?c) Enter an expression for the magnitude of the electric field ou
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Answer:
Explanation:
Total length of the wire is 29 m.
Let the length of one piece is d and of another piece is 29 - d.
Let d is used to make a square.
And 29 - d is used to make an equilateral triangle.
(a)
Area of square = d²
Area of equilateral triangle = √3(29 - d)²/4
Total area,
Differentiate both sides with respect to d.
For maxima and minima, dA/dt = 0
d = 8.76 m
Differentiate again we get the
(a) So, the area is maximum when the side of square is 29 m
(b) so, the area is minimum when the side of square is 8.76 m