Consider the force F on a charge ' q'

Question:

Consider the force $\mathrm{F}$ on a charge ' $q$ ' due to a uniformly charged 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?

  1. (1) $\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}$ for $r

  2. (2) $\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}>\mathrm{F}>0$ for $r

  3. (3) $\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}$ for $r>R$

  4. (4) $\mathrm{F}=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{R^{2}}$ for all $r$

Correct Option: , 3

Solution:

(3) For spherical shell

$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}$            (if $r \geq R$ )

$=0$                                                                                 (if $r

Force on charge in electried field, $F=q E$

$\therefore F=0 \quad($ For $r

$F=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{r^{2}}$    (For $r>R$ )

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Atin kumar
April 21, 2023, 6:35 a.m.
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