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Standard XII

Physics

Excess Pressure in Bubbles

A spherical c...

Question

A spherical conductor of radius $2 R$ has a spherical cavity of radius $\frac{R}{2}$ . The cavity does not enclose the centre of sphere. Charges $Q_{1}$ and $Q_{2}$ are placed as shown in figure, $Q_{2}$ is at the centre of cavity. An additional charges $Q_{3}$ is given to the sphere.

The potential of the sphere is

\frac{K Q_{1}}{3 R} + \frac{K (Q_{2} + Q_{3})}{2 R}

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The potential inside the cavity at a distance

r (r < \frac{R}{2})

from the centre of cavity is

\frac{K Q_{2}}{r} + \frac{5 K Q_{1}}{6 R} - \frac{3 K Q_{2}}{2 R}

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The value of potential outside the sphere at a distance

r

from the centre of sphere is

\frac{k (Q_{2} + Q_{3})}{r} + \frac{k Q_{1}}{r^{'}}

, where

^{'} r^{'}

is the distance from

Q_{1}

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The charge that will flow into ground if the sphere is grounded

Q_{2} + Q_{3} + \frac{2 Q_{1}}{3}

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Solution

The correct option is A The potential of the sphere is $\frac{K Q_{1}}{3 R} + \frac{K (Q_{2} + Q_{3})}{2 R}$

A spherical conductor $=$ $2 R$ radius.
radius $= \frac{R}{2}$
Cavity $= Q_{1}$ and $Q_{2}$
Potential $= \frac{{K Q}_{1}}{3 R} + \frac{K (Q_{1} + Q_{2})}{2 R}$

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A spherical conductor of radius 2R has a spherical cavity of radius R2. The cavity does not enclose the centre of sphere. Charges Q1 and Q2 are placed as shown in figure, Q2 is at the centre of cavity. An additional charges Q3 is given to the sphere.

The correct option is A The potential of the sphere is KQ13R+K(Q2+Q3)2RA spherical conductor = 2R radius.radius =R2Cavity =Q1 and Q2Potential =KQ13R+K(Q1+Q2)2R

A spherical conductor of radius $2 R$ has a spherical cavity of radius $\frac{R}{2}$ . The cavity does not enclose the centre of sphere. Charges $Q_{1}$ and $Q_{2}$ are placed as shown in figure, $Q_{2}$ is at the centre of cavity. An additional charges $Q_{3}$ is given to the sphere.

The correct option is A The potential of the sphere is $\frac{K Q_{1}}{3 R} + \frac{K (Q_{2} + Q_{3})}{2 R}$

A spherical conductor $=$ $2 R$ radius.
radius $= \frac{R}{2}$
Cavity $= Q_{1}$ and $Q_{2}$
Potential $= \frac{{K Q}_{1}}{3 R} + \frac{K (Q_{1} + Q_{2})}{2 R}$