if two sphere having ratio of radius 1:2and same chargeon both sphere then find ratio
of surface charge density of both sphere
Answers
Answer:
If
q
1
,
q
2
q1,q2
are the initial charges on the spheres of radil R and 2R respectively, then total charge on the two sphere
q=
q
1
+
q
2
q=q1+q2
=4π
R
2
σ+4π
(2R)
2
σ=20π
R
2
σ
=4πR2σ+4π(2R)2σ=20πR2σ
.
When the spheres are connected by a thin wire, they will share charges till their potentials become equal. The charges on the two spheres would then be in the ratio of their capacity. If
q
1
',
q
2
'
q1′,q2′
are the new values of charges on the two spheres, then
q
1
'q×
C
1
C
1
+
C
2
and
q
2
=q×
C
2
C
1
+
C
2
q1′q×C1C1+C2andq2=q×C2C1+C2
A capacity of a spherical conductor is directly proportional to the radius pf sphere,
∴
q
1
'=q×
R
R+2R
=
q
3
=
20
3
π
R
2
σ
∴q1′=q×RR+2R=q3=203πR2σ
,
q
2
'=q×
2R
R+2R
=
2q
3
=
40
3
π
R
2
σ
q2′=q×2RR+2R=2q3=403πR2σ
∴
∴
New charge density of the two spheres would be
σ
1
'=
q
1
4π
R
2
=
20
3
π
R
2
σ
4π
R
2
=
5
3
σ
σ1′=q14πR2=203πR2σ4πR2=53σ
σ
2
'=
q
2
4π
(2R)
2
=
40
3
π
R
2
σ
16π
R
2
=
5
6
Explanation: