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1. Find the electric field at point a for: a. A solid sphere of radius R carrying a volume charge density ρ b. An infinitely long, thin wire carrying a line charge density Side Cross Section C. A plane of infinite area carrying a surface charge density ơ
PoT 2. Avery long cylinder with radius a and charge density pa-is placed inside of a conducting cylindrical shell. The cylindrical shell has an inner radius of b and a thickness of t. a. Find the electric field forr < a. b. Find the electric field for a<r<b c. Find the electric field for b<r<b +t. d. Find the electric field for b+t<r. e. Plot E (r). f. Suppose the inner cylinder is known to have a total linear charge density, λ. Find the constant, po, in terms of 2 and the radius of the cylinder.
An insulating sphere of uniform charge +Q and radius a is placed inside an insulating shell of uniform charge -Q with inner radius B and outer radius C. 3. a. Find the electric field for r< a b. Find the electric field for a <r< B C. Find the electric field for B < r < c. d. Find the electric field for C < r e. Plot the electric field lines in all regions and E(r).
An insulating hollow sphere has an inner radius a and outer radius b. Within the insulating material, the volume charge density is given by ρ(r) 4. , (r) a , where α is a positive constant. r a. Find the electric field for r < a. b. Find the electric field for a<r<b c. Find the electric field forr> b. d. 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? Plot E(r). Suppose the hollow sphere is known to have a total charge Q. Find the constant, a, in terms of Q,a and b. e. f.
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Answer #1

Radius =k volume charse densidy = 8 Total charse inside the sphere - Volume & density Electric field at from the centre the kTake a gaussian Cylinder with radius au t h e and height h. Using Gauss & E. laa. & Ten E en - Charge inside the cylinder Te& Take an cylinderical gaussian (AE surface Cerith rength kat a a za and cross-sectional area = A SEA - Zen CM EA FED

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