A sphere or radius R has a charge density given by p(r') = kr'. A) Calculate...
A sphere or radius R has a charge density given by p(r') = kr'.
A) Calculate the electric field inside and out.
B) Calculate the electric potential using the integral E*dl.
C) Calculate the energy stored in this configuration by integrating pVdT.
Homework Answers
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A sphere or radius R has a charge density given by p(r') =
kr'.
A) Calculate...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows up at the center of the sphere, but falls away exponentially fast away from the center, p(r)=(C/r2)e-kr where C is an unkown constant, and k determines how fast the charge density falls off. The total charge on the sphere is Q. a) Write down the Electric Field outside the sphere, where r ≥ R, in term of the total Q. b) Show that C=...
Please help. Thank you. (3.) (40 pts) An insulating sphere of radius a has an embedded...
Please help. Thank you.
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4.1 A sphere of radius R has a uniform volume charge density ρ(r) Pr. A. Calculate...
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Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p....
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
A sphere of radius R carries a volume charge density ρ(r) = kr, where k is...
A sphere of radius R carries a volume charge density ρ(r) = kr, where k is a constant and r is in spherical coordinates. Calculate the energy of this configuration, check the answer by calculating it in four ways.
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 ,...
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 , where A is a constant and r is measured from the center of the sphere. a) Show that the electric field outside the sphere (r > R) is E = AR5 /(5εor 2 ). b) Show that the electric field inside the sphere (r < R) is E = AR3 /(5εo). Hint: The total charge Q on the sphere is found by integrating ρ...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
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A sphere of radius R has total charge Q. The volume charge density (C/m3) within the...
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. The charge within a small volume dV is dq=ρdV. The integral of ρdV over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R. Hint: Let dV be a spherical shell of radius r and thickness dr. What...
1. A very long, uniformly charged cylinder has radius R and charge density p. Determine the...
1. A very long, uniformly charged cylinder has radius R and charge density \rho. Determine the electric field of this cylinder inside (r<R) and outside (r>R)2. A large, flat, nonconducting surface carries a uniform surface charge density σ. A small circular hole of radius R has been cut in the middle of the sheet. Determine the electric field at a distance z directly above the center of the hole.3. You have a solid, nonconducting sphere that is inside of, and...
Please help. Thank you.
(3.) (40 pts) An insulating sphere of radius a has an embedded nonuniform charge den- sity: p(P) = (1+) where pe is a positive constant (this charge density is only valid for r <a). Sur- rounding the sphere, and concentric with it, is a conducting shell of inner radius b> a and outer radius c which is charged (not neutral). I do not know what the charge on the conductor is, but I am told that...
4.1 A sphere of radius R has a uniform volume charge density ρ(r) Pr. A. Calculate E(r) B. Use your answer to A to calculate V(r). C. Use your answer to B to calculate the energy of this charge configuration, via the expression U pV d where the integral must be evaluated over the bounded charge distribution. D. Use your answer to A to calculate the energy of this charge configuration, via the expression 2 2 space
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional to the square of the distance from the origin, i.e. p = kr2 for some constant k. (a) [3 marks] Calculate k if the total charge on the sphere is Q. (Hint: dt = r2 sin(O) dr do do ) (b) [3 marks) Write down Gauss's law in integral form. In which situations can it be used to directly calculate the electric field of...
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the sphere, valid at distances r >> R. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the...
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