CALC An insulating hollow sphere has inner radius a and outer radius b . Within the insulating material the volume charge density is given by ρ ( r ) = α / r , where α is a positive constant. (a) In terms of α and a , what is the magnitude of the electric field at a distance r from the center of the shell, where a < r < b ? (b) A point charge q is placed at the center of the hollow space, at r = 0. In terms of α and a , what value must q have (sign and magnitude) in order for the electric field to be constant in the region a < r < b , and what then is the value of the constant field in this region?
CALC An insulating hollow sphere has inner radius a and outer radius b . Within the insulating material the volume charge density is given by ρ ( r ) = α / r , where α is a positive constant. (a) In terms of α and a , what is the magnitude of the electric field at a distance r from the center of the shell, where a < r < b ? (b) A point charge q is placed at the center of the hollow space, at r = 0. In terms of α and a , what value must q have (sign and magnitude) in order for the electric field to be constant in the region a < r < b , and what then is the value of the constant field in this region?
CALC An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by ρ(r) = α/r, where α is a positive constant. (a) In terms of α and a, what is the magnitude of the electric field at a distance r from the center of the shell, where a < r < b? (b) A point charge q is placed at the center of the hollow space, at r = 0. In terms of α and a, what value must q have (sign and magnitude) in order for the electric field to be constant in the region a < r < b, and what then is the value of the constant field in this region?
The volume charge density of a sphere of Radius R is directly related to the radius of the sphere as given by the equation p(r) = br where b is a positive integer. What would be expression for the electric field at r = 1/2 R from the center of the sphere?
If a solid insulating sphere of radius 50 cm carries a total charge of 150 µC uniformly distributedthroughout its volume, what is its a) volume charge density? What is the magnitude of the electricfield at b) 10 cm and c) 65 cm from the center of the sphere.
If there is a a non-uniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−4r/3R)f or r≤R ρ(r)=0 for r≥R where ρ0 is a positive constant. What is the expression for the electric field in the region r <= R?
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