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Two unformly charged non conducting hemispherical sheelseach having uniform charge denstyand radius R to from a complete sphere and surround a concentric spherical conducting steel of radius R÷2. If hemispherical part are in equilibrium then minimum surface charge density of inner conducting steel is

Two unformly charged non conducting  hemispherical sheelseach having uniform charge denstyand radius R to from a complete sphere  and surround a concentric spherical conducting steel of radius R÷2. If hemispherical part are in equilibrium then minimum surface charge density of inner conducting steel is

Grade:12th pass

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
one year ago
1)
We will first find electrostatic force on right half due to first half on horizontal direction.
This will be done by integrating electrostatic pressure to all right half area

2) Then, we will calculate the force in horizontal direction by small sphere as vertical component will get cancelled out.

3) Then, we will add these two forces as 0 since right half is in equilibrium.

After calculation, minimum surface charge density of small sphere is -2£.
But, magnitude of surface charge density can be even greater than this.
But, Magnitude of Minimum is 2£.
This will be opposite in sign with given hemi
sphere.657-683_Annotation 2020-09-01 131215.png

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