A non-conducting spherical thick shell, of inner radius a and outer radius 2a, carries a charge per unit volume density. Calculate the electrostatic potential energy of this system g

Electrostatic potential energy of the given system is

U=1/4π∈*(96/5)*Q²/a

Explanation:

consider spherical shell of inner radius a  (taken as x) and outer radius 2a ,carrying charge Q and volume charge density ρ=Q/4π(2a)³...........................(1)

then voume of the shell=4πx²dx

charge on the shell inner part of the shell.q1=4πx²dx ρ

charge on this ,in case of sphereical type,q2=4/3*πx³ ρ

then electrostatic energy of sperical charge of radius a (which we taken as x) and sperical shell of radius x and thickness dx is,

dU=1/4π∈ *(q1q2)/x

by placing value of q1 and q2 from above , we will get a equation

    dU=1/4π∈*(16/3*π²ρ²x dx

then total electrostatic energy of sperical charge by integrating from limit a to 2a and putting value of ρ then we will get

U=1/4π∈*(96/5)Q²/a

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

a and c

c is 100% but i am confused in a