- #1
Quelsita
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QUESTION:
Calculate the electrostatic energy of a homogeneously charged sphere of Volume V and
compare the result with 2 times the electrostatic energy of a homogeneously charged
sphere of V/2.
SOLUTION:
OK, so we have a charge Q which is uniformly distributed within a sphere of radius, R.
We know:
q(r) is the charge in the sphere when it has
attained radius, r.
q(r)= [tex]\rho[/tex](4/3)[tex]\Pi[/tex]r3
the work done in bringing a charge dq to it is dW
dW= (q(r) dq)/(4[tex]\Pi[/tex]r[tex]\epsilon[/tex]0
dq= [tex]\rho[/tex]4[tex]\Pi[/tex]r2dr
so, we plug in the knowns:
dW= ([tex]\rho[/tex](4/3)[tex]\Pi[/tex]r3 * [tex]\rho[/tex]4[tex]\Pi[/tex]r2dr )/ (4[tex]\Pi[/tex]r[tex]\epsilon[/tex]0)
and integrate.
Is this correct thus far?
What are the limits?
Thanks!
Calculate the electrostatic energy of a homogeneously charged sphere of Volume V and
compare the result with 2 times the electrostatic energy of a homogeneously charged
sphere of V/2.
SOLUTION:
OK, so we have a charge Q which is uniformly distributed within a sphere of radius, R.
We know:
q(r) is the charge in the sphere when it has
attained radius, r.
q(r)= [tex]\rho[/tex](4/3)[tex]\Pi[/tex]r3
the work done in bringing a charge dq to it is dW
dW= (q(r) dq)/(4[tex]\Pi[/tex]r[tex]\epsilon[/tex]0
dq= [tex]\rho[/tex]4[tex]\Pi[/tex]r2dr
so, we plug in the knowns:
dW= ([tex]\rho[/tex](4/3)[tex]\Pi[/tex]r3 * [tex]\rho[/tex]4[tex]\Pi[/tex]r2dr )/ (4[tex]\Pi[/tex]r[tex]\epsilon[/tex]0)
and integrate.
Is this correct thus far?
What are the limits?
Thanks!