Question Statement:
The vector potential inside a long solenoid with n turns per unit length and carrying
current I , written in cylindrical coordinates is
(
)
0
ˆ
, ,
2
nI
A s
z
s
µ
φ
φ
=
. If the term
(
)
0
ˆ
ˆ
cos
sin
2
nI s
s
µ
α
φφ
β
φ
+
, where
0,
0
α
β
≠
≠
is added to
(
)
, ,
A s
z
φ
, the magnetic
field remains the same if
(a) α
β
=
(b) α
β
= −
(c)
2
α
β
=
(d)
2
β
α =
(
)
1
ˆ
ˆ
ˆ
Useful formulae:
;
1
1
ˆ
ˆ
ˆ
s
s
z
z
t
t
t
t
s
z
s
s
z
sv
v
v
v
v
v
v
s
z
s
z
z
s
s
s
φ
φ
φ
φ
φ
φ
φ
∂
∂
∂
∆=
+
+
∂
∂
∂
∂
∂
∂
∂
∂
∂
∇×
=
−
+
−
+
−
∂
∂
∂
∂
∂
∂
GATE 2019
I
ˆz
d
ˆx
superconductor
GATE - 2019
[SOLUTION]
Physics by fiziks
Revised Edition-2022
H.No. 40-D, G.F., Jia Sarai, Near IIT, Hauz Khas, New Delhi-16
Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com, Email: [email protected]
19
Options:
- (A) α β =
- (B) α β = −
- (C) 2 α β =
- (D) 2 β α = ( ) 1 ˆ ˆ ˆ Useful formulae: ; 1 1 ˆ ˆ ˆ s s z z t t t t s z s s z sv v v v v v v s z s z z s s s φ φ φ φ φ φ φ ∂ ∂ ∂ ∆= + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∇× = − + − + − ∂ ∂ ∂ ∂ ∂ ∂ GATE 2019 I ˆz d ˆx superconductor GATE - 2019 [SOLUTION] Physics by fiziks Revised Edition-2022 H.No. 40-D, G.F., Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498, Website: www.physicsbyfiziks.com, Email: [email protected] 19