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Sagot :
Answer: 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 [tex]x^{4}[/tex]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
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