JEE Advanced Previous Year Questions (2021 - 2024): Electric Charges and Fields | Physics for JEE Main & Advanced PDF Download

 Page 1


 
Q1: Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius
R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its
equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by:   
[ e is the permittivity of free space. ]
(a) 
q
4 pe R m
(b) 
q
32pe R m
(c) 
q
8 pe R m
(d) 
q
16pe R m
        [JEE Advanced 2024 Paper 1]
Ans: (b)
Restoring force = qE sin 
?
2
? t = qE sin 
?
2
 R = I a
E = 
Kq
(2R cos 
?
2
)²
 = 
1
4 pe
 × 
q
4R² cos² 
?
2
? 
1
4 pe
 × 
qR
4R² cos² 
?
2
 sin 
?
2
 q = mR² a
0
2
0
3
2
0
3
2
0
3
2
0
3
0
0
Page 2


 
Q1: Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius
R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its
equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by:   
[ e is the permittivity of free space. ]
(a) 
q
4 pe R m
(b) 
q
32pe R m
(c) 
q
8 pe R m
(d) 
q
16pe R m
        [JEE Advanced 2024 Paper 1]
Ans: (b)
Restoring force = qE sin 
?
2
? t = qE sin 
?
2
 R = I a
E = 
Kq
(2R cos 
?
2
)²
 = 
1
4 pe
 × 
q
4R² cos² 
?
2
? 
1
4 pe
 × 
qR
4R² cos² 
?
2
 sin 
?
2
 q = mR² a
0
2
0
3
2
0
3
2
0
3
2
0
3
0
0
For ? very small,
-q²
32pe R³ m
 ? = a
? ?² = 
q²
32 pe mR³
Hence option (B)
Q2: A small electric dipole  , having a moment of inertia I about its center, is kept at a distance r from the center of a
spherical shell of radius R. The surface charge density s is uniformly distributed on the spherical shell. The dipole is
initially oriented at a small angle ? as shown in the gure. While staying at a distance r, the dipole is free to rotate about
its center.
If released from rest, then which of the following statement(s) is(are) correct?
[ e 0 is the permittivity of free space.]
(a) The dipole will undergo small oscillations at any nite value of r.
(b) The dipole will undergo small oscillations at any nite value of r > R.
(c) The dipole will undergo small oscillations with an angular frequency of  v(2 sp 0 / e 0I) at r = 2R.
(d) The dipole will undergo small oscillations with an angular frequency of v(sp 0 / 100 e 0I) at r = 10R.    [JEE Advanced
2024 Paper 2]
0
0
Page 3


 
Q1: Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius
R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its
equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by:   
[ e is the permittivity of free space. ]
(a) 
q
4 pe R m
(b) 
q
32pe R m
(c) 
q
8 pe R m
(d) 
q
16pe R m
        [JEE Advanced 2024 Paper 1]
Ans: (b)
Restoring force = qE sin 
?
2
? t = qE sin 
?
2
 R = I a
E = 
Kq
(2R cos 
?
2
)²
 = 
1
4 pe
 × 
q
4R² cos² 
?
2
? 
1
4 pe
 × 
qR
4R² cos² 
?
2
 sin 
?
2
 q = mR² a
0
2
0
3
2
0
3
2
0
3
2
0
3
0
0
For ? very small,
-q²
32pe R³ m
 ? = a
? ?² = 
q²
32 pe mR³
Hence option (B)
Q2: A small electric dipole  , having a moment of inertia I about its center, is kept at a distance r from the center of a
spherical shell of radius R. The surface charge density s is uniformly distributed on the spherical shell. The dipole is
initially oriented at a small angle ? as shown in the gure. While staying at a distance r, the dipole is free to rotate about
its center.
If released from rest, then which of the following statement(s) is(are) correct?
[ e 0 is the permittivity of free space.]
(a) The dipole will undergo small oscillations at any nite value of r.
(b) The dipole will undergo small oscillations at any nite value of r > R.
(c) The dipole will undergo small oscillations with an angular frequency of  v(2 sp 0 / e 0I) at r = 2R.
(d) The dipole will undergo small oscillations with an angular frequency of v(sp 0 / 100 e 0I) at r = 10R.    [JEE Advanced
2024 Paper 2]
0
0
Ans: (b), (d)
The electric eld inside sphere is zero. So dipole will oscillate when r > R
Q3: A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle ? at P , as shown in
the gure. When ? = 30° , then the electric ux through the curved surface of the cylinder is F. If ? = 60° , then the
electric ux through the curved surface becomes F / vn, where the value of n is ___.   [JEE Advanced 2024 Paper 2]
Ans: 3
Solid angle made by plane surfaces:
Page 4


 
Q1: Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius
R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its
equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by:   
[ e is the permittivity of free space. ]
(a) 
q
4 pe R m
(b) 
q
32pe R m
(c) 
q
8 pe R m
(d) 
q
16pe R m
        [JEE Advanced 2024 Paper 1]
Ans: (b)
Restoring force = qE sin 
?
2
? t = qE sin 
?
2
 R = I a
E = 
Kq
(2R cos 
?
2
)²
 = 
1
4 pe
 × 
q
4R² cos² 
?
2
? 
1
4 pe
 × 
qR
4R² cos² 
?
2
 sin 
?
2
 q = mR² a
0
2
0
3
2
0
3
2
0
3
2
0
3
0
0
For ? very small,
-q²
32pe R³ m
 ? = a
? ?² = 
q²
32 pe mR³
Hence option (B)
Q2: A small electric dipole  , having a moment of inertia I about its center, is kept at a distance r from the center of a
spherical shell of radius R. The surface charge density s is uniformly distributed on the spherical shell. The dipole is
initially oriented at a small angle ? as shown in the gure. While staying at a distance r, the dipole is free to rotate about
its center.
If released from rest, then which of the following statement(s) is(are) correct?
[ e 0 is the permittivity of free space.]
(a) The dipole will undergo small oscillations at any nite value of r.
(b) The dipole will undergo small oscillations at any nite value of r > R.
(c) The dipole will undergo small oscillations with an angular frequency of  v(2 sp 0 / e 0I) at r = 2R.
(d) The dipole will undergo small oscillations with an angular frequency of v(sp 0 / 100 e 0I) at r = 10R.    [JEE Advanced
2024 Paper 2]
0
0
Ans: (b), (d)
The electric eld inside sphere is zero. So dipole will oscillate when r > R
Q3: A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle ? at P , as shown in
the gure. When ? = 30° , then the electric ux through the curved surface of the cylinder is F. If ? = 60° , then the
electric ux through the curved surface becomes F / vn, where the value of n is ___.   [JEE Advanced 2024 Paper 2]
Ans: 3
Solid angle made by plane surfaces:
O = 2 × 2 p(1 - cos ?)
? O = 4 p - 4 p cos ?
So solid angle made by curved surface: 4 p - O
= 4 p - (4 p - 4 p cos ?) = 4 p cos ?
f = f = 
4 p cos 30° Q
e
 = cos 30° 
Q
e
f = 
4 p cos 60° Q
4 p e
 = cos 60° 
Q
e
f
f
 = 
cos 30°
cos 60°
 = v3
f
f
 = v3
f = 
f
v3
 ? n = 3
Q4: An innitely long thin wire, having a uniform charge density per unit length of 5 nC/m, is passing through a spherical
shell of radius 1 m, as shown in the gure. A 10 nC charge is distributed uniformly over the spherical shell. If the
conguration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is
______.       [JEE Advanced 2024 Paper 2]
[Given: In SI units 1 / (4 pe 0) = 9 × 10 ?, ln 2 = 0.7. Ignore the area pierced by the wire.]
Ans: 171
30°
0 0
60°
0 0
30
60
60
60
Page 5


 
Q1: Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius
R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its
equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by:   
[ e is the permittivity of free space. ]
(a) 
q
4 pe R m
(b) 
q
32pe R m
(c) 
q
8 pe R m
(d) 
q
16pe R m
        [JEE Advanced 2024 Paper 1]
Ans: (b)
Restoring force = qE sin 
?
2
? t = qE sin 
?
2
 R = I a
E = 
Kq
(2R cos 
?
2
)²
 = 
1
4 pe
 × 
q
4R² cos² 
?
2
? 
1
4 pe
 × 
qR
4R² cos² 
?
2
 sin 
?
2
 q = mR² a
0
2
0
3
2
0
3
2
0
3
2
0
3
0
0
For ? very small,
-q²
32pe R³ m
 ? = a
? ?² = 
q²
32 pe mR³
Hence option (B)
Q2: A small electric dipole  , having a moment of inertia I about its center, is kept at a distance r from the center of a
spherical shell of radius R. The surface charge density s is uniformly distributed on the spherical shell. The dipole is
initially oriented at a small angle ? as shown in the gure. While staying at a distance r, the dipole is free to rotate about
its center.
If released from rest, then which of the following statement(s) is(are) correct?
[ e 0 is the permittivity of free space.]
(a) The dipole will undergo small oscillations at any nite value of r.
(b) The dipole will undergo small oscillations at any nite value of r > R.
(c) The dipole will undergo small oscillations with an angular frequency of  v(2 sp 0 / e 0I) at r = 2R.
(d) The dipole will undergo small oscillations with an angular frequency of v(sp 0 / 100 e 0I) at r = 10R.    [JEE Advanced
2024 Paper 2]
0
0
Ans: (b), (d)
The electric eld inside sphere is zero. So dipole will oscillate when r > R
Q3: A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle ? at P , as shown in
the gure. When ? = 30° , then the electric ux through the curved surface of the cylinder is F. If ? = 60° , then the
electric ux through the curved surface becomes F / vn, where the value of n is ___.   [JEE Advanced 2024 Paper 2]
Ans: 3
Solid angle made by plane surfaces:
O = 2 × 2 p(1 - cos ?)
? O = 4 p - 4 p cos ?
So solid angle made by curved surface: 4 p - O
= 4 p - (4 p - 4 p cos ?) = 4 p cos ?
f = f = 
4 p cos 30° Q
e
 = cos 30° 
Q
e
f = 
4 p cos 60° Q
4 p e
 = cos 60° 
Q
e
f
f
 = 
cos 30°
cos 60°
 = v3
f
f
 = v3
f = 
f
v3
 ? n = 3
Q4: An innitely long thin wire, having a uniform charge density per unit length of 5 nC/m, is passing through a spherical
shell of radius 1 m, as shown in the gure. A 10 nC charge is distributed uniformly over the spherical shell. If the
conguration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is
______.       [JEE Advanced 2024 Paper 2]
[Given: In SI units 1 / (4 pe 0) = 9 × 10 ?, ln 2 = 0.7. Ignore the area pierced by the wire.]
Ans: 171
30°
0 0
60°
0 0
30
60
60
60
due to wire
v - v = -2k ? ln 
2
0.5
= -2 × 9 × 10 × 3 × 10 × 2 × 0.7 = -126 V
Due to sphere:
v - v = 
kQ
2
 - 
kQ
1
 = 
-kQ
2
= 
-9 × 10 × 10 × 10
2
= -45 V
v - v = -126 - 45 = -171 V
v - v = 171 V
R P
9 -9
R P
9 -9
R P
P R