13
You visited us
13
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Physics
Area and Volume Expansion
Charge is dis...
Question
Charge is distributed within a sphere of radius R with a volume charge density
ρ
(
r
)
=
A
r
2
e
−
2
r
/
a
where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :
Open in App
Solution
According to the question
Q
=
∫
R
0
p
(
r
)
d
v
[
d
v
=
4
π
r
2
d
r
]
⇒
Q
=
∫
R
0
A
r
2
e
−
2
r
/
a
4
π
r
2
d
r
Q
=
4
π
A
∫
R
0
e
−
2
r
/
a
d
r
=
4
A
π
[
−
e
−
2
r
/
a
×
a
2
]
R
0
=
4
π
A
a
2
(
−
e
−
2
R
/
a
+
1
)
Q
=
2
π
A
a
(
1
−
e
−
2
R
/
a
)
Find radius of the sphere
1
−
e
−
2
R
/
a
=
Q
2
π
A
a
1
−
Q
2
π
A
a
=
e
−
2
R
/
a
l
n
(
1
−
Q
2
π
A
a
)
=
−
2
R
a
−
a
2
l
n
(
1
−
Q
2
π
A
a
)
=
R
R
=
a
2
l
n
(
2
π
A
a
2
π
A
a
−
Q
)
.
Suggest Corrections
0
Similar questions
Q.
Charge is distributed within a spehere of radius
R
with a volume charge density
ρ
(
r
)
=
A
r
2
e
−
2
r
/
a
,
where
A
and
a
are constants. If
Q
is the total charge of this charge distribution, the radius
R
is
Q.
A solid sphere of radius
R
has a charge
Q
distributed in its volume with a charge density
ρ
(
r
)
=
k
r
a
, where
k
and
a
are constants and
r
is the distance from its centre. If the electric field at
r
=
R
2
is
1
8
times that at
r
=
R
,
find the value of
a
.
Q.
A solid sphere of radius
R
has a charge
Q
distributed in its volume with a charge density
ρ
=
k
r
a
, where
k
and
a
are constants and
r
is the distance from its centre. If the electric field at
r
=
R
2
is
1
8
times that at
r
=
R
, the value of
a
is
Q.
A solid sphere of radius
R
has a charge
Q
distributed in its volume with a charge density
ρ
=
k
r
a
, where
k
and
a
are constants and
r
is the distance from its centre. If the electric field at
r
=
R
/
2
is 1/8 times that at
r
=
R
, find the value of
a
.
Q.
A sphere of radius
R
has charge density per unit volume,
ρ
(
r
)
=
A
(
R
−
r
)
,
for
0
<
r
<
R
( Here
A
is constant). If total electric charge inside the sphere is
Q
, then the value of
A
in terms of
Q
and
R
is
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Thermal Expansion
PHYSICS
Watch in App
Explore more
Area and Volume Expansion
Standard XII Physics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app