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  • Can someone help me with this, A point charge q is placed at a distance of r from the centre of an uncharged conducting sphere of radius R (<r). The potential at any point on the sphere is

A point charge q is placed at a distance of r from the centre of an uncharged conducting sphere of radius R (<r). The potential at any point on the sphere is

  • Option 1)

    Zero

     

     

     

  • Option 2)

    \frac{1}{4\pi \varepsilon _{0}}\cdot \frac{qR}{r^{2}}

  • Option 3)

    \frac{1}{4\pi \varepsilon _{0}}\cdot \frac{q}{r}

  • Option 4)

    \frac{1}{4\pi \varepsilon _{0}}\cdot \frac{qr^{2}}{R}

 

Answers (1)

best_answer

As we learned

 

Inside the sphere (P lies inside the sphere) -

E_{in}=0

V_{in}=constant

- wherein

 

 Since, potential V is same for all points of the sphere. Therefore, we can calculate its value at the centre of the sphere.

\therefore V=\frac{1}{4\pi \varepsilon _{0}}\cdot \frac{q}{r}+{V}'= potential at centre due to induced charge = 0 (because net induced charge will be zero)

\therefore V=\frac{1}{4\pi \varepsilon _{0}}\cdot \frac{q}{r}\cdot


Option 1)

Zero

 

 

 

Option 2)

\frac{1}{4\pi \varepsilon _{0}}\cdot \frac{qR}{r^{2}}

Option 3)

\frac{1}{4\pi \varepsilon _{0}}\cdot \frac{q}{r}

Option 4)

\frac{1}{4\pi \varepsilon _{0}}\cdot \frac{qr^{2}}{R}

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Aadil

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