The electric field at 20 cm from the centre of a
uniformly charged non-conducting sphere of radius
10 cm is E. Then at a distance 5 cm from the centre
it will be
(1) 16 E
(2) 4E
(3) 2 E
(4) Zero
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0
Answer:
Correct option is
C
2 E
For a non-conducting sphere containing a distributed charge Q and of radius R, the electric field in given by at a distance
′
r
′
E=
⎩
⎪
⎪
⎨
⎪
⎪
⎧
r
2
KQ
,
3t
0
pr
,
whenr>R(outside)fromcentre
whenr<R(inside)kwherep=
V
Q
[chargedensity]
at a distance r=20 cm, field is E(r>R) where R=10 cm (Radius of sphere)
So, E=
2O
2
KQ
⇒Q=
K
400E
=1600π∈
0
E (as K=
4π∈
0
1
)
now volume of sphere, V=
3
4
πR
3
so at a distance r=5 cm,(r<R), inside sphere :-
E
′
=
3t
0
pr
=
v3t
0
Qr
=
3
4
π×LO
3
×3×t
0
1600π∈
0
E×5
=
1000
2000E
=2E
∴E
′
=2E
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