JEE Advanced Previous Year Questions (2018 - 2025): Magnetism

Table of Contents
1. 2024
2. 2023
3. 2022
4. 2021
5. 2020
6. 2018
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2024

Q1: A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass m and radius r and it is in a uniform vertical magnetic field B₀, as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity g, on two conducting supports at P and Q. When a current I is passed through the loop, the loop turns about the line PQ by an angle θ given by:
(a) tan θ = πrIB₀ / (mg)
(b) tan θ = 2πrIB₀ / (mg)
(c) tan θ = πrIB₀ / (2mg)
(d) tan θ = mg / (πrIB₀)   

Q2: An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field B⃗. The magnitude of the line integral  along a straight line from the point (-√3a, a, 0) to (a, a, 0) is given by 
[μ₀ is the magnetic permeability of free space.] [JEE Advanced 2024 Paper 1]
(a) 7μ₀I24
(b) 7μ₀I12
(c) μ₀I8
(d) μ₀I6
Ans: (a)

[ θ₁ is anticlockwise hence taken negative] 
⇒ tanθ₁ = a√3a = √3
θ₁ = π3
⇒ tanθ₂ = aa = 1
θ₂ = π4
⇒ ∫ B ⋅ dℓ = μ₀I2π   [ π3 + π4 ]
= 7μ₀I24
⇒ Ans. Option (A)

Q3: A positive, singly ionized atom of mass number Aₘ is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width w with magnetic field  Tesla, as shown in the figure. The ion finally hits a detector at the distance x below its starting trajectory.
[Given: Mass of neutron/proton = (5/3) × 10⁻²⁷ kg, charge of the electron = 1.6 × 10⁻¹⁹ C.] [JEE Advanced 2024 Paper 2]

Which of the following option(s) is(are) correct?
(a) The value of x for H⁺ ion is 4 cm.
(b) The value of x for an ion with Aₘ = 144 is 48 cm.
(c) For detecting ions with 1 ≤ Aₘ ≤ 196, the minimum height (x₁ - x₀) of the detector is 55 cm.
(d) The minimum width w of the region of the magnetic field for detecting ions with Aₘ = 196 is 56 cm.
Ans: (a), (b)
x = 2R

Option A

Option B
For A_m = 144

Option C
For Aₘ = 1
x = 4 cm and for Aₘ = 196
x = 56 cm.
So x₀ = 4 cm and x₁ = 56 cm.
Therefore, x₁ - x₀ = 52 cm.
Option D
Minimum width = R
For Aₘ = 196.

= 28 cm

2023

Q1: A rectangular conducting loop of length  4 cm and width  2 cm is in the `xy-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction with a constant speed v. The wire is carrying a steady current  I = 10 A in the positive x-direction. A current of 10μA flows through the loop when it is at a distance  d = 4 cm from the wire. If the resistance of the loop is 0.1Ω, then the value of v is ________ ms^-1.
[Given: The permeability of free space   μ₀ = 4π × 10^-7 N A^-2 ]    [JEE Advanced 2023 Paper 2]

Ans: 4

2022

Q1: Which one of the following options represents the magnetic field  at O due to the current flowing in the given wire segments lying on the xy plane? 

(a)
(b)
(c)
(d)  [JEE Advanced 2022 Paper 2]
Ans: (c)

Q2: A small circular loop of area A and resistance R is fixed on a horizontal xy-plane with the center of the loop always on the axis  of a long solenoid. The solenoid has m turns per unit length and carries current I counterclockwise as shown in the figure. The magnetic field due to the solenoid is in  direction. List-I gives time dependences of  in terms of a constant angular frequency ω. List-II gives the torques experienced by the circular loop at time .

2021

Q1: Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I₁ in the anti-clockwise direction and the larger loop carries current I₂ in the clockwise direction, with I₂ > 2I₁. (x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?                [JEE Advanced 2021 Paper 2  ]

(a) (x, y) is perpendicular to the xy-plane at any point in the plane
(b) | (x, y) | depends on x and y only through the radial distance

(c) | (x, y) | is non-zero at all points for r < R
(d) (x, y) points normally outward from the xy-plane for all the points between the two loops
Ans: (a) & (b)

(a) Magnetic field at the plane of the ring is perpendicular to the plane. However, they bend as they move forward.

(b) By symmetry, we can say that B will be same at all the points having the same radial distance. So, B (x, y) will depend on the radial distance

(c)

, since I₂ > 2I₁, so B_net at the centre will be non-zero in ⊗ direction. But at some other point, B_net may be zero.
From the graph, it is clear that B_net = 0 for r∈(0, R).
So, option (c) is incorrect.

(d) For the graph, it is clear that B = - ve
In, ⊗ direction for r ∈ (R to 2R), so option (d) is also incorrect. 

Q2: A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at the distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure).
A resistor R = 1.4 Ω and a capacitor C₀ = 5.0μF are connected in series between the rails. At time t = 0, C₀ is uncharged. Which of the following statement(s) is(are) correct? [μ₀ = 4π × 10^-7 SI units. Take ln 2 = 0.7] 

(a) Maximum current through R is 1.2 × 10^-6 ampere
(b) Maximum current through R is 3.8 × 10^-6 ampere
(c) Maximum charge on capacitor C₀ is 8.4 × 10^-12 coulomb
(d) Maximum charge on capacitor C₀ is 2.4 × 10^-12 coulomb [JEE Advanced 2021 Paper 1]
Ans: (a) & (c)

Let a small element of length dx be chosen at a distance x  from the wire. Induced emf de across it is given by 

On substituting all the values in above, we get

At t = 0, C acts as a short. So, maximum current flows through R. 

At t → ∞,C acts as on open. So, 

Q3: A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius a, with its center at the origin. A magnetic dipole of moment m is brought along the axis of this loop from infinity to a point at distance r (>> a) from the center of the loop with its north pole always facing the loop, as shown in the figure below.
The magnitude of magnetic field of a dipole m, at a point on its axis at distance r, is , where μ₀ is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, m₁ and m₂, separated by a distance r on the common axis, with their north poles facing each other, is , where k is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles. 

When the dipole m is placed at a distance r from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to
(a) m/r³
(b) m²/r²
(c) m/r²
(d) m²/r [JEE Advanced 2021 Paper 2]
Ans: (a)

Q3: A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius a, with its center at the origin. A magnetic dipole of moment m is brought along the axis of this loop from infinity to a point at distance r (>> a) from the center of the loop with its north pole always facing the loop, as shown in the figure below.
The magnitude of magnetic field of a dipole m, at a point on its axis at distance r, is , where μ₀ is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, m₁ and m₂, separated by a distance r on the common axis, with their north poles facing each other, is , where k is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

The work done in bringing the dipole from infinity to a distance r from the center of the loop by the given process is proportional to
(a) m/r⁵
(b) m²/r⁵
(c) m²/r⁶
(d) m²/r⁷             [JEE Advanced 2021 Paper 2]
Ans: (c)

Q5: An α-particle (mass 4 amu) and a singly charged sulphur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the α-particle and the sulfur ion move in circular orbits of radii r_α and r_s, respectively. The ratio (r_s/r_α) is __________.    [JEE Advanced 2021 Paper 1]
Ans: 4

2020

Q1: A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge Q through a switch. The coil is in a horizontal uniform magnetic field Bo parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)

(a)
(b)
(c)
(d)  [JEE Advanced 2020 Paper 1]
Ans: (b)
Torque experienced by circular loop = M × B
where, M is magnetic moment and B is magnetic field.
∴ τ = iπR²NB₀
(at the instant shown θ = π/2)
∴ τdt = dL = iπR²NB₀dt
= QπR²NB₀ (∵ idt = Q) 

2018

Q1: Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R carries a constant current I₁ and the wire located at x = -R carries a constant current I₂. A circular loop of radius R is suspended with its center at (0, 0, √3R) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the direction. which of the following statements regarding the magnetic field   is (are) true?                   [JEE Advanced 2018 Paper 1]

(a) If I₁ = I₂, then cannot be equal to zero at the origin (0, 0, 0)

(b) If I₁> 0 and I₂ < 0, then  can be equal to zero at the origin (0, 0, 0)

(c) If I₁<0 and I₂ > 0, then can be equal to zero at the origin (0, 0, 0)(d) If I₁ = I₂, then the z-component of the magnetic field at the center of the loop is Ans: (a), (b) & (d)

The magnetic field at the origin O (0, 0, 0) due to the infinitely long straight wire located at x = +R is

and due to the infinitely long straight wire located at x = -R is

The magnetic field at O due to the circular loop is

The resultant magnetic field at the origin (0, 0, 0) is

Thus, if i₁ = i₂then 

If i₁ > 0 and i₂ < 0 then both are along  is along . Thus, resultant field  can be zero. 

The magnetic field  at the point C due to the infinitely long straight wire located x = +R is perpendicular to the line AC (see figure). It lies in the x-z plane and makes an angle 30∘ with the x axis. Resolve along the x and z directions to get 

Similarly, the magnetic field at C due to the infinitely long straight wire located at x = -R is 

The magnetic field at C due to the circular loop is 

The resultant magnetic field at C is 

If i₁ = i₂ then magnitudes of are equal and their z-components are equal in magnitude but opposite in direction. Thus, z-component of the magnetic field at C is due to the circular loop only and its value is .