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Suppose that the charge density of the spherical charge distribution shown in the figures below is p(r) - Po for rs Rand zero for r> R. Obtain expressions for the electric field both inside and outside the distribution. (Use any variable or symbol stated above along with the following as necessary: ,)
Gaussian
surface for E
Gaussian
surface for E
(a)
inside
outside

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An insulating sphere of radius a has a non-uniform volume charge density p = 4 where A is a constant and r is the spherical radial coordinate. This insulating sphere is surrounded by a concentric conducting spherical shell of inner and outer radii b and e, respectively (b>a) as shown in the figure. What are the induced surface charge densities on the inner (oinner) and outer (đouter) surfaces of the condueting shell? Select one: Aa Aa Oouter = Oinner = Aa dinner = Aa Oouter = - O'inner = -47Aa², 47 Aa? Oouter = 47 Aa 4 Aa Oinner = Jouter = b2 Ab Ac Oouter = Oinner = a² °
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Problem An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E =