1 Potential of concentric spheres A spherical shell with internal radius Rį and external radius R2...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge density σ(8)-k cos θ, where k is a constant and θ is the polar spherical coordinate. (a) Find the potential in each region: (i)r > b, and () a<r<b. [5 points] [Hint: start from the general solution of Laplace's equation in spherical coordinates, but allow for different coefficients in the radial part...
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -2q and the outer shell has a total charge of +4 q. Specify magnitude and direction. (a) What is the electric field for b < r < d? (b) what is the electric field for r>d?
A nonconducting sphere of radius r2 contains a concentric spherical cavity of radius r1. The material between r1 and r2 carries a uniform charge density ρE(C/m3).a) Determine the electric potential V, relative to V=0 at r=∞, as a function of the distance r from the center for r>r2. Express your answer in terms of some or all of the variables r1, r2, r, ρE, and appropriate constants.b) Determine the electric potential V, relative to V=0 at r=∞, as a function...
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 thin spherical shell with radius R1 = 4.00 cm is concentric with a larger thin spherical shell with radius 6.00 cm . Both shells are made of insulating material. The smaller shell has charge q1=+6.00nC distributed uniformly over its surface, and the larger shell has charge q2=−9.00nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells. a)What is the electric potential due to the two shells at the following...
Consider a spherical shell with inner radius a and outer radius b. A charge density σ A cos(9) is glued over the outer surface of the shell, while the potential at the inner surface of the shell is V (8) Vo cos(0). Find electric potential inside the spherical shell, a<r<b.
A small conducting spherical shell with inner radius a and outer radius bis concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of-2g and the outer shell has a total charge of +3q. Select True or False for the following statements True The total charge on the inner surface of the large shell is zero. True The total charge on the outer surface of the large shell...
A small conducting spherical shell with inner radius a and outer radius bis concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -19 and the outer shell has a total charge of +49. Select True or False for the following statements. ✓ The electric field in the region r <a is zero. The total charge on the inner surface of the large shell is +19. The...
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -1q and the outer shell has a total charge of +3q. The total charge on the inner surface of the large shell is zero. The total charge on the inner surface of the small shell is -1q. The radial component of the electric field in the region...
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -2q and the outer shell has a total charge of +4q. The total charge on the outer surface of the large shell is +2q. The radial component of the electric field in the region c <r < d is given by -2q/(4nε0r2). The total charge on...