and n 't have to

=
Now we
•
A
f- P due to dipole
apply
.

p→
npsino

} eguitorial
r
B at axial and
?
!
"
←oo- •
>✗
poos points .

• C

i.
Vp
kpysizno Vc
kPY÷
=
=
.

VB
kp%0_ kp÷Y
-

=
=
↳ -
.

i. (A) and .
AED P =
g. (d)
i. → p=q( 212) .

I
dipole moment

T =
pesina .

IX.
q(2R)E since
=
T=

ME
q(2R> C- Sino =

2-
✗ .

' '

→ Simona
Using
small
angle approximation
i. ✗ =

4,4%-0 .

i.
w=.÷÷
it to who
Comparing
a. =

i. (A) &(B) ans

and Potential is same
for all the
points of
the sphere .
Thus we calculate its value at

the center 0
of the sphere .

i. V0
¥
= .

all the
i.
This value will remain some
for
inside the conductor
points .

i. (A) ans
 d) for
and) r<a=
3£
charge
=
3cg .
i.
charge density =

}
a
.

till distance
charge
i. r

§÷aק%
i. .

i.
E=k÷ =

k(¥¥¥¥7 =

klzf.ir)

for a<r< b for b<r< c

C- =o ( conducting
C-
k↳÷ shelled :
=

k(z¥_→
net
in for r> c
E- =
charge=
.

i. (A) ans
and )
>
It .

>

>

>

distribution
charge
-

will
Inside
surface of cavity
'
be '
uneven distribution
of -

over the surface due to

asymmetric
Due to this induced
' '

placement of
.

+
q
+
+
outer
surface of
'
induced
evenly
'
will be
charge
on
, ee

Now when E- f. is switched the induced

sphere .
on ,

in
Iq will
'
outer surface move direction
of
.

on +

induced will redistribute

i. Outer
surface charge
=D
but inside won't as C-net ) conductor .

inside

i. (A) ans
and Inner will have -2sec induced and
wall
of cavity A

Total induced
of cavity charge
'

B + Inc . .
on

conductor will be -

(-2+1) = 1 rec .

i. Net potential at center

✓ + ✓ '

Value to conductor
+
cavity A cavity B

K÷
gypotontialdue
=
+ 0 +0
to
cavity
will be Zero .

9÷÷
= = 9×104

i. K=9 ans
and Heat
change
in potential energy
generated
=

of the
system .

= U
,
-

V2

V. = Initial .

i. U = KCI + k + KCI
,

212A) 2 (a)
2(a)- -
-

due to due to outer due to mutual .

shell
immer sphere

51¥ .

v2 = Final ( when conducting wire is connected , whole

shell due to
change will
go
on outer property
of conductor ) .

k(29 Kof
.

i. U, =
=

a-
2 ( za )
i. A- 4
i. Heat =
v. - u
,
= 5k£
4A
-

Kada =÷of Ans

ALI Two cases will be
formed
d) r<R,_

induced
i-Ged-ricpot-onb.ae
Y eq .

Lpn
"

¥ tog KI
=

a
-

+
-

Rz

i yrsiki.C-lectoicpoto-nhal-kof. i#+e IT .
 D) All at
=
'
charges are

R' distance
from
each other . Kq2 is
g

energy b/w
two
charges
A B i. 6 total pairs are

there in the
system .

i. U =
6kg2 ans
Tr
-

µF
q÷÷÷÷
212k) +2¥ 412

Initial
§w energy
=

¥É- ans .

"
¥-1 -15¥
""
+ .

,
✓ -
W 512
due to due to mutual
solid
sphere
shell
energy Of =

3¥22,
27kg2
6k¥ (%)
=
i. iv. D= - no
=

-20,2
=

9÷¥=6±ñ§ 4012
arid (A) E. f. is directed
along
Ez↳>E ,
i. -12

for 2>R .

& E. f. is -
ve
for 2<=0 :
→ ←
E. f. at center is zero

Casual direction
É↳
=

(A)
.

C- i i. → QRS .

F- f. f.
G > Ez for 2>R
^

Y
(B)
-
.

①
is directed towards
- > ✗
-2
i. (B) → a
②

time 1- to plane
(c) potential at center is Zero and
of
also i. ④ →p
ring & passing through
center is 0