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AIEEE 2012 Solved Paper
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© examsnet.com
Question : 44
Total: 89
This question has statement- 1 and statement- 2. Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius
R
has a uniformly positive charge density
ρ
. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.
Statement- 1 : When a charge
q
is take from the centre of the surface of the sphere its potential energy changes by
q
ρ
3
ε
0
Statement- 2 : The electric field at a distance
r
(
r
<
R
)
from the center of the sphere is
ρ
r
3
ε
0
.
Statement- 1 is true, Statement- 2 is true; Statement- 2 is not the correct explanation of Statement- 1.
Statement 1 is true, Statement 2 is false.
Statement 1 is false, Statement 2 is true.
Statement- 1 is true, Statement- 2 is true; Statement- 2 is the correct explanation of Statement-1.
Validate
Solution:
The electric field inside a uniformly charged sphere is
=
ρ
.
r
3
E
0
The electric potential inside a uniformly charged sphere
=
ρ
R
2
6
∈
0
[
3
−
r
2
R
2
]
∴
Potential difference between center and surface
=
ρ
R
2
6
E
0
[
3
−
2
]
=
ρ
R
2
6
E
0
∆
U
=
q
ρ
R
2
6
E
0
© examsnet.com
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