Shells , ill are conducting spherical neutral
shells of radius R 2R and 3R respectively
Shell and shell lll are connected. A point
charge do is kept at centre O. Now Shell It is
also grounded
R
R
The charge on surface b' (outer surface of
Shell I) is
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Class 12
>>Physics
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>>Electrostatics of Conductors
>>Three concentric spherical shells have r
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Three concentric spherical shells have radii r, 2r, and 3r. Innermost and outermost shells are earthed. Now charges on the shells are q
1
, q
2
and q
3
respectively. Then :
This question has multiple correct options
Hard
Solution
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Verified by Toppr
Correct options are A) , B) and C)
Step 1: General Formula of Potential of Sphere of Radius R
At outside point at a distance x from its centre,
V
x
=
x
Kq
At inside point, it is constant, same as that over its surface,
V
inside
=
R
Kq
Step 2: Potential at sphere (1) and sphere (3) [Ref. Fig.]
Potential being a scalar quantity, it will be added due to all the spheres at a point.
So, Potential at sphere (1)
V
1
=V
Self
+V
By Sph. 2
+V
By Sph. 3
⇒ V
1
=
r
Kq
1
+
2r
Kq
2
+
3r
Kq
3
....(1) (For spheres 2 & 3, sphere 1 is a inside point, so using formula accordingly)
Potential at sphere (3)
V
3
=V
By Sph. 1
+V
By Sph. 2
+V
Self
⇒ V
3
=
3r
Kq
1
+
3r
Kq
2
+
3r
Kq
3
....(2) (For spheres 1 & 2, sphere 3 is a outside point, so using formula accordingly)
Step 3: Earthing of sphere (1) and sphere (3)
On earthing potential becomes zero:
Therefore, from equation (1), V
1
=0
⇒
r
Kq
1
+
2
+
3r