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Q 26. 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 × 10^{3} 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)
Solution: Magnetic susceptibility is
Q 27. 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 xaxis, while segments PS and QN are parallel to the yaxis. 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 ( μ_{0} = 4π × 10^{−7}N / A^{2} ) [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)
Solution:
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 28. A proton and an αparticle (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)
Solution:
Kinetic energy = qΔV
Q 29. A paramagnetic material has 10^{28} atoms/m^{3}. 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 30. The mean intensity of radiation on the surface of the Sun is about 10^{8} W/m^{2}. The rms value of the corresponding magnetic field is closest to [2019]
(1) 1 T
(2) 10^{2} T
(3) 10^{−2} T
(4) 10^{−4} T
Ans: (4)
Solution:
Intensity of EM wave is
As we know that
Q 31. 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 32. 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 – ω^{2}Rcos^{2}φ
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 33. 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 34. A uniform magnetic field B of 0.3 T is along the positive Zdirection. 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 35. 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 36. 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 B_{0} 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 37. 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)
Solution:
Q 38. 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 σ_{1 }and σ_{2} are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)
[2016]
(2) σ_{1} = σ_{2} =ε_{0}vB
(4) σ_{1} =ε_{0}vB, σ_{2} = ε0vB
Ans: (4)
Solution:
direction of is towards left therefore induced change dentition will be electric field =
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