The energy stored in a charged sphere can be calculated from the volume charge density, which is equal to the total charge Q divided by the volume of the sphere. The expression for the electric potential inside the sphere is Q/4πε0r for r < R, and Q/4πε0R for r = R, where R is the radius. The total energy of the sphere can be obtained by integrating the expression for dU= (3Q/4πε0R3)r2dr from r=0 to R. This gives the final expression for the total electric field energy of the sphere as U=Q2/30πε0R.
The energy stored in a charged sphere can be calculated from the volume charge density, which is equal to the total charge Q divided by the volume of the sphere. The expression for the electric potential inside the sphere is Q/4πε0r for r < R, and Q/4πε0R for r = R, where R is the radius. The total energy of the sphere can be obtained by integrating the expression for dU= (3Q/4πε0R3)r2dr from r=0 to R. This gives the final expression for the total electric field energy of the sphere as U=Q2/30πε0R.
The energy stored in a charged sphere can be calculated from the volume charge density, which is equal to the total charge Q divided by the volume of the sphere. The expression for the electric potential inside the sphere is Q/4πε0r for r < R, and Q/4πε0R for r = R, where R is the radius. The total energy of the sphere can be obtained by integrating the expression for dU= (3Q/4πε0R3)r2dr from r=0 to R. This gives the final expression for the total electric field energy of the sphere as U=Q2/30πε0R.
The energy stored in a charged sphere can be calculated from the volume charge density, which is equal to the total charge Q divided by the volume of the sphere. The expression for the electric potential inside the sphere is Q/4πε0r for r < R, and Q/4πε0R for r = R, where R is the radius. The total energy of the sphere can be obtained by integrating the expression for dU= (3Q/4πε0R3)r2dr from r=0 to R. This gives the final expression for the total electric field energy of the sphere as U=Q2/30πε0R.
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The energy stored in a sphere can calculated interms
of volume charge density,
dU V r r Volume charge density of the sphere is, q 4 R3 3 Here, q is the charge and R is the radius of the sphere. The expresion for potential of the sphere inside is, Q Qr 3 V r 4 0 r R 3 Q r2 4 0 R 3 Then, 1 r2 dU 3 4 r 2 dr 4 0 R 1 r 2 3Q dU 4 r dr 2 4 0 R 3 4 R 3 1 r 2 3Q 2 3 3 r dr 4 0 R R 3Q 1 4 6 r dr 4 0 R The total energy of the sphere can be obtained by intigrating the above equation betwen the limits 0 to R. R 3Q 2 6 U field r 4 dr 0 4 0 R 3Q 2 R 5 4 0 R 6 5 1 3 Q2 4 0 5 R