If the energy stored in a spherical conductor having a charge of 12 {C} is 6 J , then the radius of the spherical conductor is [AP EAPCET 23 May 2025 S2]

Correct Answer is : 10.8cm10.8 {cm}10.8cm

Correct Answer is : 10.8cm10.8 {cm}10.8cm

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Electrostatics

Section: Physics

Question : 2 of 32

Marks: +1, -0

12 \mu \mathrm{C}

Solution:

The energy stored in a capacitor is given by the formula:

U=\frac{q^2}{2C}

where

U

is energy,

q

is charge, and

C

is capacitance.

Step 2: Rearranging to Find Capacitance

We can solve for

C

as follows:

C=\frac{q^2}{2U}

Here,

q=12 \times 10^{-6} \mathrm{C}

and

U=6 \mathrm{J}

. Substitute these values into the formula:

C=\frac{(12 \times 10^{-6})^2}{2 \times 6}

Step 3: Calculate Capacitance

Simplify the above equation:

C=12 \times 10^{-12} \mathrm{F}

Step 4: Capacitance of a Spherical Conductor

The capacitance of a spherical conductor is given by:

C=4 \pi \varepsilon_0 r

Step 5: Find the Radius

Rearrange to find the radius

r: r=\frac{C}{4 \pi \varepsilon_0}

We can also use

\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{N m^2 / C^2}

so:

r=9 \times 10^9 \times 12 \times 10^{-12}

Step 6: Solve for the Radius

Multiply the values:

r=108 \times 10^{-3}=0.108 \mathrm{m}=10.8 \mathrm{cm}

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