JEE Main Previous Year Questions (2016- 2025): Moving Charges & Magnetism- 2

Q.28. A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of 20 × 10^-6 J/T when a magnetic intensity of 60 × 10³ A/m is applied. Its magnetic susceptibility is    [2019]
(1) 3.3 × 10^-2
(2) 4.3 × 10^-2
(3) 2.3 × 10^-2
(4) 3.3 × 10^-4 

Ans: (4)
Magnetic susceptibility is

Q.29. As shown in the figure, two infinitely long, identical wires are bent by 90° and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4 cm, and the magnitude of the magnetic field at O is 10^-4 T, and the two wires carry equal currents (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ( μ₀ = 4π × 10^-7N / A² )    [2019]
(1) 20 A, perpendicular out of the page
(2) 40 A, perpendicular out of the page
(3) 20 A, perpendicular into the page
(4) 40 A, perpendicular into the page

Ans: (3)
Magnetic field at O will be done by PS and QN
Given OP = OQ = 4 × 10^-2 
Magnetic field at point O is B_net = 10^-4 T
Magnetic field at Point O due to wire LP and MQ is zero.
Let current in each wire = i
Thus, B_net = B_PS + B_QN     (both inward)

Therefore, current is 20 A and it is perpendicular into the page.

Q.30. A proton and an α-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii r_p : r_α of the circular paths described by them will be    [2019]
(1) 1 : √2
(2)1 : 2
(3) 1 : 3
(4) 1 : √3

Ans: (1)
Kinetic energy = qΔV

Q.31. A paramagnetic material has 10²⁸ atoms/m³. Its magnetic susceptibility at temperature 350 K is 2.8 × 10^-4. Its susceptibility at 300 K is    [2019]
(1) 3.267 × 10^-4
(2) 3.672 × 10^-4
(3) 3.726 × 10^-4
(4) 2.672 × 10^-4

Ans: (1)
Solution:
where, T_C = Curie's Temperature

Q.32. The mean intensity of radiation on the surface of the Sun is about 10⁸ W/m². The rms value of the corresponding magnetic field is closest to     [2019]
(1) 1 T
(2) 10² T
(3) 10^-2 T
(4) 10^-4 T

Ans: (4)
Intensity of EM wave is

As we know that

Q.33. An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_e, r_p, r_α respectively in a uniform magnetic field B. The relation between r_e, r_p, r_α is:    [2018]
(1) r_e > r_p = r_α
(2) r_e < r_p = r_α
(3) r_e < r_p < r_α
(4) r_e < r_α < r_p

Ans: (2)
Solution:

Q.34. Suppose that the angular velocity of rotation of earth is increased. Then as a consequence:    [2018]
(1) Weight of the object every where on the earth will decrease
(2) Weight of the object every where on the earth will increase
(3) Except at poles weight of the object on the earth will decrease
(4) There will be no change in weight anywhere on the earth

Ans: (3)
Solution:
g' = g - ω²Rcos²φ
Where φ is latitude there will be no change in gravity at poles as φ = 90°
At all other points as ω increases g' will decrease

Q.35. In a certain region static electric and magentic fields exist. The magnetic field is given by If a test charge moving with a velocityexperiences no force in that region, then the electric field in the region, in SI units, is -    [2017]
(1)
(2)
(3)
(4)

Ans: 4
Solution:
F_e = F_n = 0
F_{e =} -F_m

Q.36. A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm × 5 cm carries a current I of 12 A. Out of the following different orientations, which one corresponds to stable equilibrium ?    [2017]
(1)
(2)
(3)
(4)

Ans: 3
Solution:
For the 3rd option figure,
M = NIA
are on same direction

Q.37. Two identical wires A and B, each of length  '', carry the same current I. Wire A is bent into a circle of radius R and wire B is bent to form a square of side 'a'. If BA and BB are the values of magnetic field at the centres of the circle and square respectively, then the ratio BA / BB is:    [2016]
(1)
(2)
(3)
(4)

Ans: (4)

Q.38. A conducting metal circular - wire loop of radius r is placed perpendicular to a magnetic field which varies with time as B =B0e^-t/τ, where B₀ and ^τ are constants, at t = 0 . If the resistance of the loop is R then the heat generated in the loop after a long time (t →∞) is :    [2016]

Ans: (4)
Solution:

Q.39. A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is 240 ms^-1 The earth's magnetic field over Delhi is 5 × 10^-5 T with the declination angle ~0° and dip of θ such that sinθ =  2/3. If the voltage developed is V_B between the lower and upper side of the plane and V_W. between the tips the wings then V_B and V_W are closed to:      [2016]
(1) V_B = 40 mV, V_W = 135 mV with left side of pilot at higher voltage
(2) V_B = 40 mV, V_W = 135 mV with right side of pilot at high voltage
(3) V_B = 45 mV, V_W = 120 mV with left side of pilot at higher voltage
(4) V_B = 45 mV, V_W = 120 mV with right side of pilot at higher voltage

Ans: (3)

Q.40. Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed 'v' in a uniform magnetic field B going into the plane of the paper (see figure) . If charge densities σ₁ and σ₂ are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)
      [2016]

(2) σ₁ = σ₂ =ε₀vB

(4) σ₁ =ε₀vB, σ₂ = -ε0vB

Ans: (4)

direction of  is towards left therefore induced change dentition will be electric field =