Question

Two concentric metal spheres have radii 9.5 cm and 10.3 cm, respectively. The inner sphere has a charge of 6 nC spread uniformly on its surface, and the outer sphere has charge −6 nC on its surface. Find the total energy stored in the electric field inside the spheres. Approximate the spheres as parallel flat slabs separated by 0.8 cm . The permittivity of free space is 8.8542 × 10−12 C 2 /N · m 2 . Answer in units of nJ.

Answer 1

The total energy stored in the electric field inside the spheres is 1696.1 nJ.

Step-by-step explanation:

Given that,

Radius of inner sphere = 9.5 cm

Radius of outer sphere = 10.3 cm

Charge of inner sphere = 6nC

Charge of outer sphere = -6nC

We need to calculate the potential for inner sphere

Using formula of potential

`V_(in)=(Q)/(4\pi\epsilon_(0)R)`

Put the value into the formula

`V_(in)=(9*10^(9)*6*10^(-9))/(9.5*10^(-2))`

`V_(in)=568.4\ V`

Potential for outer sphere,

`V_(out)=(9*10^(9)*6*10^(-9))/(10.3*10^(-2))`

`V_(out)=-524.3\ V`

We need to calculate the capacitor

Using formula of capacitor

`Q=CV`

`C=(Q)/(V)`

Where, Q = charge

V = potential difference

Put the value into the formula

`C=(6*10^(-9))/(568.4)`

`C=1.05*10^(-11)\ C/V`

We need to calculate the total energy stored in the electric field inside the spheres

Using formula of store energy

`E=(1)/(2)CV^2`

Put the value into the formula

`E=(1)/(2)*1.05*10^(-11)*(568.4)^2`

`E=0.00000169616244\ J`

`E=1696.1*10^(-9)\ J`

`E=1696.1 nJ`

Hence, The total energy stored in the electric field inside the spheres is 1696.1 nJ.