Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 22, Problem 45P
(a)
To determine
The total charge on the shell.
(b)
To determine
The expressions for electric field everywhere.
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Chapter 22 Solutions
Physics for Scientists and Engineers
Ch. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - Prob. 9PCh. 22 - Prob. 10P
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- Consider a neutral conducting sphere with radiusRthat has a sphericalcavity of radiusRcin the middle, and a point charge +qat the center of thecavity. We define the position of the point charge as the origin. The sphereis placed in a region that has a spatially homogeneous external electricfieldEext=E0k,wherekis the unit vector inz-direction. Consider thefollowing problems using the spherical coordinate system (r,✓,').(a) Determine the electric potentialV(r,✓,') in the region 0<r<Rc(b) Determine the electric potentialV(r,✓,') in the regionRc<r<R(c) Determine the electric potentialV(r,✓,')everywhereintheregionr>R.Hint: This may be easiest to solve as a boundary valueproblem with the help ofV(r,✓)=P1n=0(Anrn+Bn/rn+1)Pn(cos(✓)),wherePn(cos(✓)) are Legendre polynomials.(d) Determine the surface charge density(✓,') on the outersurface of the conductor.arrow_forwardA long cylinder of aluminum of radius R meters is charged so that it has a uniform charge per unit length on its surface of λ . (a) Find the electric field inside and outside the cylinder. (b) Plot electric field as a function of distancefrom the center of the rod.arrow_forwardO Macmillan Learning A sphere of radius R₁ = 0.340 m and uniform charge density -43.5 μC/m³ lies at the center of a neutral, spherical, conducting shell of inner and outer radii R₂ = 0.558 m and R3 = 0.770 m, respectively. Find the surface charge density on the inner and outer surfaces of the shell. inner surface charge density: 1.83 outer surface charge density: 96 μC/m² μC/m² | R₁ R₂ R3arrow_forward
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