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A pair of thin spherical shells with radius r and R, r < R are arranged to share a center. What is the capacitance of the system. If a potential difference V is created between the shells, how much energy is stored between them?

Respuesta :

Answer:

Capacitance =  ( 4π×∈×r×R ) / (R-r)

energy store =   ( 4π×∈×r×R )×V²  / (R-r)

Explanation:

given data

radius = r

radius  = R

r < R

to find out

capacitance and how much energy store

solution

we consider here r is inner radius and R is outer radius

so now apply capacitance C formula that is

C = Q/V    .................1

here Q is charge and V is voltage

we know capacitance have equal and opposite charge so

V = [tex]\int\limits^R_r {E} \, dx[/tex]  

here E = Q / 4π∈k²

so

V = Q / 4π∈ [tex]\int\limits^R_r {1/k^2} \, dx[/tex]

V = Q / 4π∈ × ( 1/r - 1/R )

V = Q(R-r)  /   ( 4π×∈×r×R )

so from equation 1

C = Q/V

Capacitance =  ( 4π×∈×r×R ) / (R-r)

and

energy store is  1/2×C×V²

energy store =   ( 4π×∈×r×R )×V²  / (R-r)

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