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  • Consider the force F on a charge 'q' due to a uniformly charged a spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the

Consider the force F on a charge 'q' due to a uniformly charged a spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?  
Option: 1 F=\frac{1}{4\pi \epsilon _{0}}\; \frac{Qq}{r^{2}}\; for\; r>R
 
Option: 2 \frac{1}{4\pi \epsilon _{0}}\; \frac{qQ}{R^{2}}\;>F>0\; for\; r<R
Option: 3 F=\frac{1}{4\pi \epsilon _{0}}\; \frac{Qq}{r^{2}}\; for\; r<R  
Option: 4 F=\frac{1}{4\pi \epsilon _{0}}\; \frac{Qq}{r^{2}} for all r

Answers (1)

best_answer

\\ \text{Inside the shell} \mathrm{E}=0$ hence $F=0$ \\ Oustside the sheell $\mathrm{E}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{Q}}{\mathrm{r}^{2}}$

\begin{array}{l} \mathrm{E}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{Q}}{\mathrm{r}^{2}} \\ \\ \text { hence } \mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{Qq}}{\mathrm{r}^{2}} \text { for } \mathrm{r}>\mathrm{R} \end{array}

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Deependra Verma

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