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Problem 1

Suppose that the Faraday concentric sphere experiment is performed in free space using a central charge at the origin, Q1, and with hemispheres of radius a. A second charge Q2 (this time a point charge) is located at distance R from Q1, where R>>a.(a) What is the force on the point charge before the hemispheres are assembled around Q1? (b) What is the force on the point charge after the hemispheres are assembled but before they are discharged? ( c ) What is the force on the point charge after the hemispheres are assembled and after they are discharged? ( d ) Qualitatively, describe what happens as Q2 is moved toward the sphere assembly to the extent that the condition R>>a is no longer valid.

Problem 2

An electric field in free space is E=(5z2/ϵ0)a^z V/m. Find the total charge contained within a cube, centered at the origin, of 4m side length, in which all sides are parallel to coordinate axes (and therefore each side intersects an axis at ±2 ).

Problem 3

The cylindrical surface ρ=8 cm contains the surface charge density, ρS= 5e20|z|nC/m2.(a) What is the total amount of charge present? (b) How much electric flux leaves the surface \(\rho=8 \mathrm{~cm}, 1 \mathrm{~cm}

Problem 6

In free space, a volume charge of constant density ρv=ρ0 exists within the region \(-\infty

Problem 7

Volume charge density is located in free space as ρv=2e1000rnC/m3 for \(0

Problem 8

Use Gauss's law in integral form to show that an inverse distance field in spherical coordinates, D=Aar/r, where A is a constant, requires every spherical shell of 1 m thickness to contain 4πA coulombs of charge. Does this indicate a continuous charge distribution? If so, find the charge density variation with r.

Problem 9

A uniform volume charge density of 80μC/m3 is present throughout the region \(8 \mathrm{~mm}10 \mathrm{~mm}\), find Dr at r=20 mm.

Problem 10

An infinitely long cylindrical dielectric of radius b contains charge within its volume of density ρv=aρ2, where a is a constant. Find the electric field strength, E, both inside and outside the cylinder.

Problem 12

The sun radiates a total power of about 3.86×1026 watts (W). If we imagine the sun's surface to be marked off in latitude and longitude and assume uniform radiation, (a) what power is radiated by the region lying between latitude 50N and 60N and longitude 12W and 27W?(b) What is the power density on a spherical surface 93,000,000 miles from the sun in W/m2?

Problem 13

Spherical surfaces at r=2,4, and 6 m carry uniform surface charge densities of 20nC/m2,4nC/m2, and ρso, respectively. (a) Find D at r=1, 3 , and 5 m. (b) Determine ρS0 such that D=0 at r=7 m.

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