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

Answer:

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

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

$V_{in}=\dfrac{Q}{4\pi\epsilon_{0}R}$

Put the value into the formula

$V_{in}=\dfrac{9\times10^{9}\times6\times10^{-9}}{9.5\times10^{-2}}$

$V_{in}=568.4\ V$

Potential for outer sphere,

$V_{out}=\dfrac{9\times10^{9}\times6\times10^{-9}}{10.3\times10^{-2}}$

$V_{out}=-524.3\ V$

We need to calculate the capacitor

Using formula of capacitor

$Q=CV$

$C=\dfrac{Q}{V}$

Where, Q = charge

V = potential difference

Put the value into the formula

$C=\dfrac{6\times10^{-9}}{568.4}$

$C=1.05\times10^{-11}\ C/V$

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

Using formula of store energy

$E=\dfrac{1}{2}CV^2$

Put the value into the formula

$E=\dfrac{1}{2}\times1.05\times10^{-11}\times(568.4)^2$

$E=0.00000169616244\ J$

$E=1696.1\times10^{-9}\ J$

$E=1696.1 nJ$

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