Question

What is the energy density in the electric field at the surface of a 2.70-cm-diameter sphere charged to a potential of 2000V ?

______________ J/m³

Answer 1

v=2000 V
r=2.7 cm=0.027 m
let energy density be U

U=W/V [V=volume,W=energy]
U=0.5cv^2/A*r [c=capacitance,v=voltage,A=area,r=radius...
U=(0.5E0A/r)v^2/(A*r) [c=E0A*r where E0= permittivity of vacuum]
U=0.5E0v^2/r^2
U=0.5E0*E^2 [E=electric field ,E=v/r]

U=0.5*8.875*10^-12*(v^2/r^2)
U=0.5*8.875*10^-12*(2000/0.027)^2
U=0.065 J/m^3

Answer 2

v=2000 V
r=2.7 cm=0.027m
let energy density be U

U=W/V [V=volume,W=energy]
U=0.5cv^2/A*r [c=capacitance,v=voltage,A=area,r=radius...
U=(0.5E0A/r)v^2/(A*r) [c=E0A*r where E0= permittivity of vacuum]
U=0.5E0v^2/r^2
U=0.5E0*E^2 [E=electric field ,E=v/r]

U=0.5*8.875*10^-12*(v^2/r^2)
U=0.5*8.875*10^-12*(2000/0.027)^2
U=0.0243 J/m^3