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JEE Main Physics Class 12 Electrostatic Potential and Capacitance Part 1 Questions
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© examsnet.com
Question : 75
Total: 100
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 centre of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinite is zero.
Statement -1
When a charge q is taken from the centre to 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 centre of the sphere is
ρ
r
3
ε
0
.
[2012]
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 potential energy at the centre of the sphere
U
c
=
3
2
K
Q
q
R
The potential energy at the surface of the sphere
U
s
=
K
q
Q
R
Now change in the energy
Δ
U
=
U
c
−
U
s
=
K
Q
q
R
[
3
2
−
1
]
=
K
Q
q
2
R
Where
Q
=
ρ
.
V
=
ρ
.
4
3
π
R
3
Δ
U
=
2
K
3
π
R
3
ρ
q
R
Δ
U
=
2
3
×
1
4
π
∈
0
π
R
3
ρ
q
R
Δ
U
=
R
2
ρ
q
6
∈
0
Using Gauss's law
∫
→
E
.
→
d
A
=
q
e
n
E
0
=
β
×
4
3
π
R
3
E
0
⇒
∫
E
d
A
(
cos
θ
)
=
β
×
4
π
R
3
3
E
0
⇒
E
(
4
π
R
2
)
=
β
×
4
3
π
R
3
×
1
E
0
⇒
E
=
β
r
3
E
0
(
r
<
R
)
© examsnet.com
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