Moving Charges & Magnetism PYQs Set 17 (PDF)

Set 17 of 19 · Questions 481-510 of 549

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Mere Teacher · Previous Year Questions JEE Main Physics · Moving Charges & Magnetism · Set 17 (Q481-510)
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481. $Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle 'θ' with the vertical. If wires have mass λ per unit length then the value of I is : (g = gravitational acceleration)$ (1) $sin θ \frac{πλgL}{μ _{0} cosθ}$ (2) $2 sin θ \frac{πλgL}{μ _{0} cosθ}$ (3) $2 \frac{πgL}{μ _{0}} tan θ$ (4) $\frac{πλgL}{μ _{0}} tan θ$ 482. $A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :$ (1) $2.5 sec, 5 sec$ (2) $5 sec, 7.5 sec$ (3) $2.5 sec, 7.5 sec$ (4) $10 sec, 5 sec$ 483. $A particle of mass m and charge q has an initial velocity v \to= v_{o} j^. If an electric field E \to= E_{o} i^and magnetic field B \to= B_{o} i^act on the particle, its speed will double after a time :$ (1) $t = \frac{m v _{0} 3}{qE}$ (2) $t = \frac{m v _{0} 2}{qE}$ (3) $t = \frac{m v _{0}}{qE}$ (4) $t = \frac{m v _{0}}{2 qE}$ 484. $An insulating thin rod of length l has a linear charge density ρ (x) = ρ_{0} \frac{x}{l} on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is:$ (1) $πnρ l^{3}$ (2) $\frac{π}{3} nρ l^{3}$ (3) $\frac{π}{4} nρ l^{3}$ (4) $n ρ l^{3}$ 485. $A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be [NEET 2016]$ (1) $\frac{μ _{0} Ii}{2 π}$ (2) $\frac{2 μ _{0} IiL}{3 π}$ (3) $\frac{μ _{0} IiL}{2 π}$ (4) $\frac{2 μ _{0} Ii}{3 π}$ 486. $In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:$ (1) $outside the cable$ (2) $inside the outer conductor$ (3) $inside the inner conductor$ (4) $in between the two conductors$ 487. $A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from + ve z direction and lying in xy plane in shown in figure. The plot of j component of magnetic field (By) at a distance 'a' (less than radius of the coil) and on yz plane vs z coordinate look like$ (1) (2) (3) (4) 488. $The resistance of an ammeter is 13 Ω and its scale is graduated for a current upto 100 amps. After an additional shunt has been connected to this ammeter it becomes possible to measure currents upto 750 amperes by this meter. The value of shunt‐resistance is$ (1) $2 Ω$ (2) $0.2 Ω$ (3) $2 kΩ$ (4) $20 Ω .$ 489. $An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is:$ (1) $\frac{h}{π e B}$ (2) $\frac{2 h}{πeB}$ (3) $\frac{h}{2 πeB}$ (4) $\frac{4 h}{πeB}$ 490. $When a charge of 3 C is placed in uniform electric field, it experiences a force of 3000 N . Within this field, potential difference between two points separated by a distance of 1 cm is$ (1) $10 V$ (2) $90 V$ (3) $1000 V$ (4) $3000 V$ 491. $A particle ’ P ’ is formed due to a completely inelastic collision of particles ’ x ’ and ’ y ’ having de-Broglie wavelengths ’ γ_{x} ’, and ’ γ_{y} ’' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of ’ P ’ is:$ (1) $\frac{γ _{x} γ _{y}}{γ _{x} + γ _{y}}$ (2) $\frac{γ _{x} γ _{y}}{γ _{x} - γ _{y}}$ (3) $γ_{x} - γ_{y}$ (4) $γ_{x} + γ_{y}$ 492. $A solenoid of length 0.4 m and having 500 turns of wire carries a current 3 A. A thin coil having 10 turns of wire and radius 0.1 m carries current 0.4 A. The torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is (μ_{0} = 4 π \times 1 0^{- 7} SI units, π^{2} = 10) (sin 9 0^{\circ} = 1)$ (1) $3 \times 1 0^{- 6} N m$ (2) $12 \times 1 0^{- 6} N m$ (3) $6 \times 1 0^{- 6} N m$ (4) $24 \times 1 0^{- 6} N m$ 493. $The magnetic field (B) inside a long solenoid having n, turns per unit length and carrying current I when iron core is kept in it is (μ_{0} = permeability of vacuum, χ = magnetic susceptibility)$ (1) $μ_{0} ∋ (1 - χ)$ (2) $μ_{0} n t^{'} γ$ (3) $μ_{0} n I^{2} (1 + χ)$ (4) $μ_{0} n I (1 + χ_{1})$ 494. $An alternating electric field, of frequency u, is applied across the dees (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by$ (1) $B = m νe and K = 2 m π^{2} v^{2} R^{2}$ (2) $B = \frac{2 πm ν}{e} and K = m^{2} π$ (3) $B = \frac{2 π m ν}{e} and K = 2 m π^{2} ν^{2} R^{2}$ (4) $B = \frac{m ν}{e} and K = m^{2} π νR2$ 495. $A charged particle is moving in a uniform magnetic field (2 i + 3 j) T. If it has an acceleration (α i - 4 j) m/s^{2}, then the value of α will be$ (1) $3$ (2) $6$ (3) $12$ (4) $2$ 496. $A particle of charge q and mass m is moving with a velocity - v i^(v \neq = 0) towards a large screen placed in the Y - Z plane at a distance d . If there is a magnetic field B = B_{0} k^, the minimum value of v for which the particle will not hit the screen is$ (1) $\frac{2 q d B _{0}}{m}$ (2) $\frac{q d B _{0}}{3 m}$ (3) $\frac{q d B _{0}}{2 m}$ (4) $\frac{q d B _{0}}{m}$ 497. $A solenoid having area A and length ' l' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is:$ (1) $\frac{B ^{2} A l}{4 μ _{0}}$ (2) $\frac{B ^{2} A l}{2 μ _{0}}$ (3) $\frac{B ^{2} A l}{μ _{0}}$ (4) $B^{2} Al$ 498. $A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed: (A) By changing the magnitude of the magnetic field within the coil. (B) By changing the area of coil within the magnetic field. (C) By changing the angle between the direction of magnetic field and the plane of the coil. (D) By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below:$ (1) $A and B only$ (2) $A, B and C only$ (3) $A, B and D only$ (4) $A and C only$ 499. $A current loop in a magnetic field$ (1) $can be in equilibrium in two orientations, both the equilibrium states are unstable.$ (2) $can be in equilibrium in two orientations, one stable while the other is unstable.$ (3) $experiences a torque whether the field is uniform or non uniform in all orientations.$ (4) $can be in equilibrium in one orientation.$ 500. $A cyclotron is used to accelerate$ (1) $only positively charged particles$ (2) $both positively and negatively charged particles$ (3) $neutron$ (4) $only negatively charged particles.$ 501. $Given below are two statements Statement I: Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only. Statement II: Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q. In light of above statements choose the most appropriate answer from the options given below. [NEET 2022]$ (1) $Both Statement I and Statement II are incorrect.$ (2) $Statement I is correct and Statement II is incorrect.$ (3) $Statement I is incorrect and Statement II is correct.$ (4) $Both Statement I and Statement II are correct.$ 502. $Pick out the wrong statement.$ (1) $The gain in the K.E. of the electron moving at right angles to the magnetic field is zero.$ (2) $When an electron is shot at right angles to the electric field, it traces a parabolic path.$ (3) $An electron moving in the direction of the electric field gains K.E.$ (4) $An electron at rest experiences no force in the magnetic field$ 503. $An electron is moving along the positive x-axis. If uniform magnetic field is applied parallel to the negative z-axis, then (A) The electron will experience magnetic force along positive y-axis (B) The electron will experience magnetic force along negative y-axis (C) The electron will not experience any force in magnetic field (D) The electron will continue to move along the positive x-axis (E) The electron will move along circular path in magnetic field Choose the correct answer from the option given below:$ (1) $A and E only$ (2) $C and D only$ (3) $B and E only$ (4) $B and D only$ 504. $In a cyclotron a charged particle$ (1) $speeds up in dee$ (2) $undergoes acceleration all the time$ (3) $slows down within a dee and speeds up between dees$ (4) $speeds up between the dees because of the magnetic field.$ 505. $In a moving coil galvanometer, two moving coils M_{1} and M_{2} have the following particulars: R_{1} = 5Ω, N_{1} = 15, A_{1} = 3.6 \times 10^{- 3} m^{2}, B_{1} = 0.25 T R_{2} = 7Ω, N_{2} = 21, A_{2} = 1.8 \times 10^{- 3} m^{2}, B_{2} = 0.50 T Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of M_{1} and M_{2} ?$ (1) $1 : 1$ (2) $1 : 3$ (3) $1 : 2$ (4) $1 : 4$ 506. $Consider a moving coil galvanomenter (MCG): (A) The torsional constant in moving coil galvanometer has dimentions (ML^{2} T^{- 2}) (B) Increasing the current sensitivity may not necessarily increase the voltage sensitivity. (C) If we increase number of turns (N) to its double (2 N), then the voltage sensitivity doubles. (D) MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. (E) Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below:$ (1) $A, D Only$ (2) $A, B, E Only$ (3) $B, D, E Only$ (4) $A, B Only$ 507. $Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If Oxygen ion (O^{- 2}) and Hydrogen ion (H^{+}) enter normal to the magnetic field with equal momentum, then the path of O^{- 2} ion has a smaller curvature than that of H^{+} . Reason R: A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. In the light of the above statements, choose the correct answer from the options given below$ (1) $Both A and R are true but R is NOT the correct explanation of A$ (2) $A is false but R is true$ (3) $A is true but R is false$ (4) $Both A and R are true and R is the correct explanation of A$ 508. $A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is :(A) maximum at either ends of the conductor and minimum at the midpoint(B) maximum at the axis of the conductor(C) minimum at the surface of the conductor(D) minimum at the axis of the conductor(E) same at all points in the cross-section of the conductor Choose the correct answer from the options given below:$ (1) $(A), (D) Only$ (2) $(D) Only$ (3) $(E) Only$ (4) $(B), (C) Only$ 509. $Consider a long thin conducting wire carrying a uniform current I. A particle having mass \" \" and charge \" \" is released at a distance \" \" from the wire with a speed along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance from the wire. The value of is [ is vacuum permeability]$ (1) $a e^{- \frac{4 π m v _{0}}{q μ _{0}}}$ (2) $a [1 - \frac{m v _{0}}{2 q μ _{0} I}]$ (3) $a [1 - \frac{m v}{q μ _{0} I}]$ (4) $\frac{a}{2}$ 510. $A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per meter in the solenoid is . [Take mass of electron m_{e} = 9 \times 10^{- 31} kg, charge of electron (q_{e}) = 1.6 \times 10^{- 19} C, (μ_{0} = 4 π \times 10^{- 7} \frac{N}{A ^{2}}, 1 ns = 10^{- 9} s)$