The electric potential on the surface of a charged spherical conductor of radius $5 \mathrm{~cm}$ is $200 \mathrm{~V}$. Work done in moving a charge of $+5 \mathrm{C}$ from a point $A$ to another point $B$ situated at distances of $15 \mathrm{~cm}$ and $10 \mathrm{~cm}$ respectively…

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The electric potential on the surface of a charged spherical conductor of radius $5 \mathrm{~cm}$ is $200 \mathrm{~V}$. Work done in moving a charge of $+5 \mathrm{C}$ from a point $A$ to another point $B$ situated at distances of $15 \mathrm{~cm}$ and $10 \mathrm{~cm}$ respectively from the centre of the sphere is

Aicharya · Accepted Answer

Electric potential on the surface of sphere, $V=200 \mathrm{~V}$ Radius, $R=5 \mathrm{~cm}=5 \times 10^{-2} \mathrm{~m}$ Charge, $q=5 \mathrm{C}$

Electric potential on the surface of sphere, $\begin{aligned} V & =9 \times 10^9 \frac{Q}{R} \\ 200 & =9 \times 10^9 \cdot \frac{Q}{5 \times 10^{-2}} \Rightarrow Q=\frac{10^{-8}}{9} \mathrm{C} \end{aligned}$ Work done to move the charge from point $A$ to point $B$ is given as $\begin{aligned} W & =V_{A B} \cdot q \\ & =\left(V_B-V_A\right) q=\left(9 \times 10^9 \cdot \frac{Q}{r_B}-9 \times 10^9 \cdot \frac{Q}{r_A}\right) 5 \\ & =9 \times 10^9\left(\frac{10^{-8}}{9 \times 10^{-1}}-\frac{10^{-8}}{9 \times 15 \times 10^{-2}}\right) 5 \\ & =45 \times 10^9 \times 10^{-8}\left[\frac{1}{9 \times 10^{-1}}-\frac{1}{9 \times 15 \times 10^{-2}}\right] \end{aligned}$ $\begin{aligned} & =450 \times \frac{1}{9}\left[10-\frac{100}{15}\right]=50\left[\frac{50}{15}\right] \\ & =166.66 \mathrm{~J}=166.7 \mathrm{~J} \end{aligned}$

The electric potential on the surface of a charged spherical conductor of radius \(5 \mathrm{~cm}\) is \(200…

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