Question

Two conducting spheres of radii 'r' and 'ra'
have equal surface charge densities. The ratio
of their charge is :​

Answer 1

GiveN :

• Two sphere are of Radius r and ra
• Surfaces Densities are equal

To FinD :

• Ratio of their Charges

SolutioN :

$\sf{For\ First\ Sphere} \begin{cases} \tt{Radius\ =\ r} \\ \\ \tt{Surface\ density\ =\ \sigma_1} \\ \\ \tt{Charge\ =\ q_1} \end{cases}$

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$\sf{For\ Second\ Sphere} \begin{cases} \tt{Radius\ =\ ra} \\ \\ \tt{Surface\ density\ =\ \sigma_2} \\ \\ \tt{Charge\ =\ q_2} \end{cases}$

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If Surface Densities are equal then,

$\dashrightarrow \tt{\sigma_1\ =\ \sigma_2} \\ \\ \\ \dashrightarrow \tt{\dfrac{dq_1}{\cancel{4\ \pi\ } r^2}\ =\ \dfrac{dq_2}{\cancel{4\ \pi\ } (ra)^2}} \\ \\ \\ \dashrightarrow \tt{\dfrac{q_1}{\cancel{r^2}}\ =\ \dfrac{q_2}{\cancel{r^2} a^2}} \\ \\ \\ \dashrightarrow \tt{q_1\ =\ \dfrac{q_2}{a^2}} \\ \\ \\ \dashrightarrow \tt{\dfrac{q_1}{q_2}\ =\ \dfrac{1}{a^2}} \\ \\ \\ \\ \implies \underline{\boxed{\sf{Ratio\ =\ 1\ :\ a^2}}}$