Two identical metal spheres A, B possessing charges 50μC and -100μC respectively are kept in contact and then separated. What will be the new charges on A, B?
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12th
Physics
Electric Charges and Fields
Applications of Gauss Law
Two metal spheres, one of r...
PHYSICS
Two metal spheres, one of radius R and the other of radius 2R, both have same surface charge density σ. If they are brought in contact and separated, then the new surface charge densities on each of the sphere are respectively
December 26, 2019avatar
Paramesh Arora
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Before contact, charges of each spheres,
q
1
=σ4πR
2
;q
2
=σ4π(2R)
2
=4q
1
When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V
1
=V
2
∴
4πε
0
R
q
1
′
=
4πε
0
(2R)
q
2
′
∴q
2
′
=2q
1
′
....(i)
As there is no loss of charge in the process
∴q
1
′
+q
2
′
=q
1
+q
2
=q
1
+4q
1
=5q
1
=5(σ4πR
2
)
or q
1
′
+2q
1
′
=5σ4πR
2
(using (i))
q
1
′
=
3
5
σ4πR
2
;q
2
′
=2q
1
′
=
3
10
(σ4πR
2
)
σ
1
=
4πR
2
q
1
′
=
3
5
σ,σ
2
=
4π(2R)
2
q
2
′
=
6
5
σ