Question

If the capacitance of a spherical conductor is 4 μF, then radius of sphere will be

3.6 x 10³ m

4 x 10³ m

3.6 x 10¹ m

9 x 10³ m​

Answer 1

Given:

The capacitance of a spherical conductor is 4 μF.

To find:

Radius of sphere ?

Calculation:

• The general expression of the capacitance of an isolated sphere is as follows:

$C = 4\pi \epsilon_{0}(r)$

• Here 'r' is radius of the sphere.

Now, putting the values in SI UNITS:

$\implies 4 \times {10}^{ - 6} = 4\pi \epsilon_{0}(r)$

$\implies 4 \times {10}^{ - 6} = \dfrac{r}{9 \times {10}^{9} }$

$\implies r = 4 \times 9 \times {10}^{( 9 - 6)}$

$\implies r = 36\times {10}^{3}$

$\implies r = 3.6\times {10}^{ 4} \: m$

So, radius of sphere is 3.6 × 10⁴ metres.

Answer 2

HELLO DEAR,

GIVEN:- If the capacitance of a spherical conductor  is 4 μF, then radius of sphere will be

          A) 3.6 x 10⁴A)  m

          B) 4 x 10³ m

          C) 3.6 x 10¹ m

          D) 9 x 10³ m

SOLUTION:- The capacitance of  an isolated spherical conductor of radius 'r' is given by

  $\bold{C=\:4π\epsilon_{0}r}$

   

       According to question,

                     

    $\bold{C=\:4π\epsilon_{0}r}$ =   4μF

        4μF = 4 × 10⁻⁶

   So,

    $\bold{4π\epsilon_{0}r}$ = 4 × 10⁻⁶

  $\bold{r}$ = $\bold{\frac{4×10^{-6}}{4π\epsilon_{0}}}$

              $\bold{r}$ = $\bold{4×10^{-6}\: × 9×10^{9}}$

             

             $\bold{r}$ = $\bold{3.6×10^{4}}$

 Therefore, option A) 3.6× 10⁴ is correct.

THANKS.