A uniformly charged conducting sphere of $4.4$ $\mathrm{m}$ diameter has a surface charge density of 60 $\mu…

A uniformly charged conducting sphere of $4.4$ $\mathrm{m}$ diameter has a surface charge density of 60 $\mu C \mathrm{~m}^{-2}$. The charge on the sphere is
  1. $7.3 \times 10^{-3} C$
  2. $3.7 \times 10^{-6} \mathrm{C}$
  3. $7.3 \times 10^{-6} C$
  4. $3.7 \times 10^{-3} C$

Solution

Here, $D=2 r=4.4 \mathrm{~m}$, or $=r=2.2 \mathrm{~m}$
$\sigma=60 \mu \mathrm{C} m^{-2}$
Charge on the sphere, $q=\sigma \times 4 \pi r^{2}$ $=60 \times 10^{-6} \times 4 \times \frac{22}{7} \times(2.2)^{2}=3.7 \times 10^{-3} \mathrm{C}$

Asked in: JEE Mains - Electrostatics - Test 2

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