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9. Electric Field Inside an Insulator (25 pts.) A spherical insulator has constant charge density, total...
3. A solid spherical insulator with radius Ry is surrounded by a conducting spherical shell with...
3. A solid spherical insulator with radius Ry is surrounded by a conducting spherical shell with inner radius R2 and outer radius R3 and with the same center point as the central sphere. The central sphere has charge density p yr3, where r is the distance from the common center of the sphere and shell. The conducting shell has charge Q. Find the magnitude of the electric field as a function of r in the following regions: R2 (a)r s...
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...
Item 25 The electric field was defined as E - Fon a/g, and we used this...
Item 25 The electric field was defined as E - Fon a/g, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g of a point mass? Write your answer using the unit vector , but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive Newton's law of gravity and Coulomb's law are botlh inverse-square laws. Consequently, there should be a "Gauss's law...
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=...
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...
A solid, insulating sphere of radius a has a uniform charge density ρ and a total charge Q
Guided Problem 4 -Gauss's LawA solid, insulating sphere of radius a has a uniform charge density ρ and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the following figure. (a) Find the magnitude of the electric field in the regions: r<a, a<r<b, and r>c. (b) Determine the induced charge per unit area on the inner and outer surfaces of the hollow sphere.Solution scheme:...
An infinitely long insulating cylinder of radius R has a volume charge density that varies with...
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as p po (a-where po a and b are positive constants and ris the distance from the axis of the cylinder. Use Gauss's law to determine the magnitude of the electric field at radial distances (a) r< R and (b)r>R
A non-uniformly charged sphere of radius R has a total charge Q. The electric field inside...
A non-uniformly charged sphere of radius R has a total charge Q. The electric field inside this charge distribution is described by E=Emax(r4 /R4 ), where Emax is a known constant. Using the differential form of Gauss’s law, find volume charge density as a function of r. Express your result in terms of r, R and Emax.
A sphere has a total charge Q uniformly distributed over its volume. The field inside the...
A sphere has a total charge Q uniformly distributed over its volume. The field inside the sphere at a radius r is given by Er= k (Q/R^3) r (a) What is the electric field at a radius r from the center of the sphere, where r > R (i.e outside of the sphere)? (b) Write down an expression for the electric potential at a radius r for r > R (i.e. outside of the sphere). (c) What is the electric...
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge...
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge density ρ 0 if r > R where γ is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin. c) Use the integral form of Gauss's law to determine the electric field in the region r < R. (Hint: if the charge distribution is spherically symmetric, what...
3. A solid spherical insulator with radius Ry is surrounded by a conducting spherical shell with inner radius R2 and outer radius R3 and with the same center point as the central sphere. The central sphere has charge density p yr3, where r is the distance from the common center of the sphere and shell. The conducting shell has charge Q. Find the magnitude of the electric field as a function of r in the following regions: R2 (a)r s...
Item 25 The electric field was defined as E - Fon a/g, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g of a point mass? Write your answer using the unit vector , but be careful with signs; the gravitational force between two "like masses" is attractive, not repulsive Newton's law of gravity and Coulomb's law are botlh inverse-square laws. Consequently, there should be a "Gauss's law...
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...
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as p po (a-where po a and b are positive constants and ris the distance from the axis of the cylinder. Use Gauss's law to determine the magnitude of the electric field at radial distances (a) r< R and (b)r>R
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge density ρ 0 if r > R where γ is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin. c) Use the integral form of Gauss's law to determine the electric field in the region r < R. (Hint: if the charge distribution is spherically symmetric, what...
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