Two spheres A & B of radii $4 \mathrm{~cm} \& 6 \mathrm{~cm}$ are given charges of $80 \mu \mathrm{C} \& 40…

Two spheres A & B of radii $4 \mathrm{~cm} \& 6 \mathrm{~cm}$ are given charges of $80 \mu \mathrm{C} \& 40 \mu \mathrm{C}$ respectively. If they are connected by a fine wire, the amount of charge flowing from one to the other is
  1. $32 \mu \mathrm{C}$ from B to A
  2. $32 \mu \mathrm{C}$ from A to B
  3. $20 \mu \mathrm{C}$ from A to B
  4. $16 \mu \mathrm{C}$ from B to A

Solution


$\mathrm{Q}_1=80 \mu \mathrm{C}, \mathrm{Q}_2=40 \mu \mathrm{C}$ $\mathrm{r}_1=4 \mathrm{~cm}, \mathrm{r}_2=6 \mathrm{~cm}$ $\therefore \quad$ After connecting wire, $\mathrm{Q}_1^{\prime}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_1+\mathrm{r}_2}\right)\left(\mathrm{Q}_1+\mathrm{Q}_2\right)=\left(\frac{4}{4+6}\right)(80+40)=48 \mu \mathrm{C}$ $\therefore \quad$ Charge flow from A to B is $\Delta \mathrm{Q}=\mathrm{Q}_1-\mathrm{Q}_1^{\prime}=80-48=32 \mu \mathrm{C}$

Asked in: AP EAMCET 2024 (20 May Shift 1)

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