Question

In: Physics

A nonconducting spherical shell of inner radius a = 2.00 cm and outer radius b =...

A nonconducting spherical shell of inner radius a = 2.00 cm and outer radius b = 2.40 cm has (within its thickness) a positive volume charge density p = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of charge q = 4.5 x 10 ^ -14 C is located at the center of that center. Find the total charge of the shell.

Solutions

Expert Solution

Consider a gaussian sphere of thickness inside the spherical shell at a distance from the center.

Volume of spherical shell with thickness is

Charge in the volume is

Charge on the spherical shell is

------(1)

Charge enclosed in the gaussian sphere is ( q is at center)

Electric field at a distance from the center is due to the charge on spherical shell and charge at center.

Flux

Electric field must be uniform, so to keep electric field uniform

Substituting the value of A and in the equation (1)

Total charge of the spherical shell is

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A solid spherical shell with a 12.0 cm inner radius and 15.0 cm outer radius is...

A solid spherical shell with a 12.0 cm inner radius and 15.0 cm outer radius is filled with water. A heater inside the water maintains the water at a constant temperature of 350 K. The outer surface of the shell is maintained at 280 K. The shell is made of Portland cement, which has a thermal conductivity of 0.29 W/(mK). (a) Starting from the basic equation for thermal conduction, derive the rate at which heat flows out of the water....

A small conducting spherical shell with inner radius a and outer radius b is concentric with...

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. Select True or False for the following statements. 1. The total charge on the inner surface of the small shell is -4q. 2. The total charge on the outer surface of the...

A small conducting spherical shell with inner radius a and outer radius b is concentric with...

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. Select True or False for the following statements. The total charge on the inner surface of the small shell is zero. True False The total charge on the inner surface of the large...

A conducting spherical shell with inner radius a=0.1 m and outer radius b=0.5 m has a...

A conducting spherical shell with inner radius a=0.1 m and outer radius b=0.5 m has a positive point charge Q=+5 nC located in its center. The total charge on the shell is -3Q and it is insulated from its surroundings. a. Calculate the surface charge density on the surfaces of the shell. b. Calculate the magnitude of the electric field at a radius of 0.01 m, and at a radius of 1.5 m. c. Sketch the electric field lines in...

A spherical shell has inner radius RinRin and outer radius RoutRout. The shell contains total charge...

A spherical shell has inner radius RinRin and outer radius RoutRout. The shell contains total charge QQ, uniformly distributed. The interior of the shell is empty of charge and matter. Part A Find the electric field strength outside the shell, r≥Routr≥Rout. Part B Part complete Find the electric field strength in the interior of the shell, r≤Rinr≤Rin. Part C Find the electric field strength within the shell, Rin≤r≤RoutRin≤r≤Rout.

A capacitor consists of two concentric spherical shells. The outer radius of the inner shell is...

A capacitor consists of two concentric spherical shells. The outer radius of the inner shell is a = 0.1 m and the inner radius of the outer shell is b = 0.2 m. a. What is the capacitance, C, of this capacitor? b. Suppose the maximum possible electric field at the outer surface of the inner shell before the air starts to ionize E max(r=a) = 3.0*10^6 V/m . What is the maximum possible charge on the inner capacitor? c....

An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density...

An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density ρ=6r C/m4. (a) (2 pts.) Based on the symmetry of the situation, describe the Gaussian surface (if any) that could be used to find the electric field inside the spherical shell. (b) (3 pts.) Starting from the definition of charge enclosed, briefly derive the integral expression for the charge enclosed inside a Gaussian surface within the insulated spherical shell for the given charge density....

A non-conducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume...

A non-conducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density p through the shell. Use Gauss's Law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the sphere. Your answer should be in terms of p,R1,R2,r Eo, and pi. a). r < R1 b.) R1 <r<2 c.) r>R2

A coaxial cable has length d, inner wire radius a and outer shell radius b. You...

A coaxial cable has length d, inner wire radius a and outer shell radius b. You can regard its capacitance and inductance to be in series. If charge +q is placed on the inner wire with −q on the outer shell, how much time will elapse before you will find −q on the inner wire and +q on the outer shell?

A cylinder of radius 4.09 cm and a spherical shell of radius 7.47 cm are rolling...

A cylinder of radius 4.09 cm and a spherical shell of radius 7.47 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the cylinder\'s angular speed to the spherical shell\'s angular speed be?

Subjects