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Q3: Find the electric field inside a spherical sphere which carries a charge density proportional to...
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...
Find the field inside and outside a sphere of radius R, which carries a volume charge...
Find the field inside and outside a sphere of radius R, which carries a volume charge density purpo. Find Qenclosed for a Gaussian shape inside and outside the charge distribution. Find SE da for a Gaussian shape inside and outside the charge distribution.
9. Electric Field Inside an Insulator (25 pts.) A spherical insulator has constant charge density, total...
9. Electric Field Inside an Insulator (25 pts.) A spherical insulator has constant charge density, total charge > 0, and radius B. What is the magnitude of the electric field at a distance B/2 from the center of the sphere? Give the answer in terms of Q, B, and K, where K is the constant from Coulomb's law. Hint: Use Gauss's law.
A spherical ball of radius R1 is charged with a constant charge density ρ. However a...
A spherical ball of radius R1 is charged with a constant charge density ρ. However a smaller spherical hollow region of radius R2 is located at the center. Show that the electric field E inside the hollow region is uniform and find the electric field. When the electric field at any point in the cavity is equal to the electric field produced by the big sphere with uniform charge density ρ plus the electric field produced by the cavity with...
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p.
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p. A spherical cavity of radius b is removed from sphere which is a distance z from the center of the sphere. Assume that a > z + b. a) Find the magnitude and direction of the electric field at point y0 which is separated by distance yo from the center of the sphere. b) Find the magnitude and direction of the electric field...
You have constructed an arrangement with a nonconducting sphere of radius R inside a thin conducting spherical shell. You have managed to distribute a uniform charge density p inside the nonconducting...
You have constructed an arrangement with a nonconducting sphere of radius R inside a thin conducting spherical shell. You have managed to distribute a uniform charge density p inside the nonconducting sphere. Find the electrostatic field inside the nonconducting sphere and outside of the arrangement of sphere and shell. What is the surface charge density on the inner surface of the conducting shell?
1. Find the electric field at point a for: a. A solid sphere of radius R...
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...
Electric charge is distributed over the xy-plane, with density inversely proportional to the distance from the...
Electric charge is distributed over the xy-plane, with density inversely proportional to the distance from the origin. Show that the total charge inside a circle of radius R centered at the origin is proportional to R. What is the constant of proportionality?
2d 3. A conducting spherical shell of radius d carries a positive charge +Q which is...
2d 3. A conducting spherical shell of radius d carries a positive charge +Q which is surrounded by an insulating sphere of radius 2d and charge -Q. Charge density of the insulating sphere is given by p. Calculate the electric field strength in terms of Q for (i) r < d, (ii) d <r<2d, (ii) r > 2d where r is the distance from the origin. (iv) Plot the variation of electric field as a function of r for d...
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...
Find the field inside and outside a sphere of radius R, which carries a volume charge density purpo. Find Qenclosed for a Gaussian shape inside and outside the charge distribution. Find SE da for a Gaussian shape inside and outside the charge distribution.
9. Electric Field Inside an Insulator (25 pts.) A spherical insulator has constant charge density, total charge > 0, and radius B. What is the magnitude of the electric field at a distance B/2 from the center of the sphere? Give the answer in terms of Q, B, and K, where K is the constant from Coulomb's law. Hint: Use Gauss's law.
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...
2d 3. A conducting spherical shell of radius d carries a positive charge +Q which is surrounded by an insulating sphere of radius 2d and charge -Q. Charge density of the insulating sphere is given by p. Calculate the electric field strength in terms of Q for (i) r < d, (ii) d <r<2d, (ii) r > 2d where r is the distance from the origin. (iv) Plot the variation of electric field as a function of r for d...
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