Moving Charges & Magnetism PYQs Set 18 (PDF)

Set 18 of 19 · Questions 511-540 of 549

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Mere Teacher · Previous Year Questions JEE Main Physics · Moving Charges & Magnetism · Set 18 (Q511-540)
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511. $A current of 1.5A is flowing through a triangle, of side 9cm each. The magnetic field at the centroid of the triangle is: (Assume that the current is flowing in the clockwise direction.)$ (1) $3 \times 1 0^{- 7} T, outside the plane of triangle$ (2) $23 \times 1 0^{- 7} T, outside the plane of triangle$ (3) $23 \times 1 0^{- 5} T, inside the plane of triangle$ (4) $3 \times 1 0^{- 5} T, inside the plane of triangle$ 512. $As shown in the figure, a current of 2A flowing in an equilateral triangle of side 43 cm. The magnetic field at the centroid O of the triangle is: (Neglect the effect of earth's magnetic field.)$ (1) $43 \times 1 0^{- 4} T$ (2) $43 \times 1 0^{- 5} T$ (3) $3 x 1 0^{- 4} T$ (4) $33 \times 1 0^{- 5} T$ 513. $A conducting wire is in the shape of a regular hexagon which is inscribed inside an imaginary circle of radius R . If a current I flows the wire, the magnitude of magnetic field at the centre of the circle is$ (1) $\frac{μ _{0} I}{2 3 π R}$ (2) $\frac{3 μ _{0} I}{2 π R}$ (3) $\frac{3 μ _{0} I}{2 π R}$ (4) $\frac{3 μ _{0} I}{πR}$ 514. $A particle of mass m and charge q is in an electric and magnetic field given by E = 2 i^+ 3 j^; B = 4 j^+ 6 k^. The charged particle is shifted from the origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the total work done is:$ (1) $5q$ (2) $(2.5)q$ (3) $(0.35) q$ (4) $(0.15)q$ 515. $A straight wire of length 0.5 meter and carrying a current of 1.2 ampere is placed in uniform magnetic field of induction 2 tesla. The magnetic field is perpendicular to the length of the wire. The force on the wire is$ (1) $2.4 N$ (2) $1.2 N$ (3) $3.0 N$ (4) $2.0 N$ 516. $Statement (I): A uniform electric field and a uniform magnetic field are pointed in the same direction. If an electron is projected in the same direction the electron velocity will decrease in magnitude. Statement (II): Two infinite long parallel wires are carrying current in the same direction. The magnetic field at a point midway between the wires is zero. Statement (III): No net force acts on a rectangular coil carrying a steady current when suspended in a uniform magnetic field. Which of the following is correct?$ (1) $Statements I, II and III are true.$ (2) $Statements I and II are true, but statement III is false.$ (3) $Statements II and III are true, but statement I is false.$ (4) $Statements I and III are true, but statement II is false.$ 517. $The magnetic moment of a diamagnetic atom is$ (1) $much greater than one$ (2) $one$ (3) $between zero and one$ (4) $equal to zero$ 518. $Given below are two statements: One is labeled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason (R): Moving charged particle experiences magnetic force perpendicular to its direction of motion.$ (1) $Both (A) and (R) are true and (R) is the correct explanation of (A)$ (2) $Both (A) and (R) are true but (R) is NOT the correct explanation of (A)$ (3) $(A) is true but (R) is false$ (4) $(A) is false but (R) is true.$ 519. $Among the following, Ampere's circuital law is represented by$ (1) $\oint B \cdot dl = 0$ (2) $\oint B \cdot dl = μ_{0} I$ (3) $\oint B \cdot dl = \frac{μ _{0}}{I}$ (4) $\oint B \cdot dl = μ_{0}$ 520. $A rod with circular cross-section area 2 c m^{2} and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is 4 π x10-6Wb. The relative permeability of the rod is (Given: Permeability of vacuum μ_{0} = 4 π \times 1 0^{- 7} N A^{- 2})$ (1) $12.5$ (2) $\frac{32}{5}$ (3) $125$ (4) $\frac{5}{16}$ 521. $Two long parallel conductors S_{1} and S_{2} are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of 3 π coulomb is passing through the point P with velocity v = (2 i + 3 j) m / s; where x & y represents unit vector along x & y axis respectively. The force acting on the charge particle is 4 π \times 1 0^{- 5} (- x i + 2 j) N . The value of x is:$ (1) $2$ (2) $1$ (3) $3$ (4) $-3$ 522. $The magnetic susceptibility negative for$ (1) $paramagnetic and ferromagnetic materials$ (2) $diamagnetic material only$ (3) $paramagnetic material only$ (4) $ferromagnetic material only$ 523. $In which of the following case no force exerted by a magnetic field on a charge?$ (1) $Moving with constant velocity$ (2) $Moving in a circle$ (3) $At rest$ (4) $Moving along a curved path$ 524. $A current loop in a magnetic field:$ (1) $can be in equilibrium in one orientation$ (2) $can be in equilibrium in two orientations, both the equilibrium states are unstable$ (3) $can be in equilibrium in two orientations, one stable while the other is unstable$ (4) $experiences a torque whether the field is uniform or non uniform in all orientate$ 525. $Two infinitely long thin wires are placed at (1 cm, 0 cm) and (2 cm, 0 cm) as shown in the figure. The same current i flows in both the wires in the same direction, say, into the page. Let the magnetic field at the origin due to these wires is B . If B_{0} is the magnitude of the magnetic field if only the wire at (1 cm, 0 cm) was present, then the value of B / B_{0} is$ (1) $3/2$ (2) $2/3$ (3) $½$ (4) $2$ 526. $A particle having a mass of 1 0^{- 2} kg carries a charge of 5 \times 1 0^{- 8} C. The particle is given an initial horizontal velocity of 1 0^{5} m s^{- 1} in the presence of electric field E and magnetic field B. To keep the particle moving in a horizontal direction, it is necessary that (A) B should be perpendicular to the direction of velocity and E should be along the direction of velocity (B) Both B and E should be along the direction of velocity (C) Both B and E are mutually perpendicular and perpendicular to the direction of velocity (D) B should be along the direction of velocity and E should be perpendicular to the direction of velocity. Which one of the following pairs of statements is possible?$ (1) $(A) and (C)$ (2) $(C) and (D)$ (3) $(B) and (C)$ (4) $(B) and (D)$ 527. $A particle having a mass of 10-2 kg carries a charge of 5 \times 10-8 C. The particle is given an initial horizontal velocity of 105 m s^{-1} in the presence of electric field E and magnetic field B . To keep the particle moving in a horizontal direction, it is necessary that (i) should be perpendicular to the direction of velocity and E should be along the direction of velocity (ii) Both B and E should be along the direction of velocity (iii) Both B and E are mutually perpendicular and perpendicular to the direction of velocity. (iv) B should be along the direction of velocity and E should be perpendicular to the direction of velocity Which one of the following pairs of statements is possible$ (1) $(i) and (iii)$ (2) $(iii) and (iv)$ (3) $(ii) and (iii)$ (4) $(ii) and (iv)$ 528. $A charge Q is uniformly distributed over the surface of non-condcting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity ω. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. if we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure:$ (1) (2) (3) (4) 529. $Position of an ant (S in metres) moving in Y - Z plane is given by S = 2 t^{2} j + 5 k (where t is in second). The magnitude and direction of velocity of the ant at t = 1 s will be :$ (1) $16 m / s in y-direction$ (2) $4 m / s in x -direction$ (3) $9 m / s in z-direction$ (4) $4 m / s in y -direction$ 530. $The electrostatic force (F_{1}) and magnetic force (F_{2}) acting on a charge q moving with velocity v can be written :$ (1) $F_{1} = q E, F_{2} = q (V \times B)$ (2) $F_{1} = q B, F_{2} = q (B \times V)$ (3) $F_{1} = q E, F_{2} = q (B \times V)$ (4) $F_{1} = q V \cdot E, F_{2} = q (B \cdot V)$ 531. $A circular coil has moment of inertia 0.8 kgm^{2} around any diameter and is carrying current to produce a magnetic moment of 20 Am^{2} . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical, it starts rotating, around its horizontal diameter. The angular speed the coil acquires after rotating by 60^{\circ} will be$ (1) $10 rad s^{- 1}$ (2) $10 π rad s^{- 1}$ (3) $13.16 rad s^{- 1}$ (4) $20 π rad s^{- 1}$ 532. $Uniform magnetic fields of different strengths (B_{1} and B_{2}), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q, at the interface at an instant, moves into the region 2 with velocity v and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface? (Consider the velocity of the particle to be normal to the magnetic field and B_{2} > B_{1})$ (1) $\frac{mv}{q B _{1}} (1 - \frac{B _{1}}{B _{2}}) \times 2$ (2) $\frac{mv}{q B _{1}} (1 - \frac{B _{2}}{B _{1}}) \times 2$ (3) $\frac{mv}{q B _{1}} (1 - \frac{B _{2}}{B _{1}})$ (4) $\frac{mv}{q B _{1}} (1 - \frac{B _{1}}{B _{2}})$ 533. $A charge ' q ' moves with velocity ' v ' through electric (E) as well as magnetic field (B). Then the force acting on it is$ (1) $q (v \times B)$ (2) $q (B \times v)$ (3) $q(v\cdotB)$ (4) $q E + q (v \times B)$ 534. $Two short bar magnets of length 1 cm each have magnetic moments 1.20 A m^{2} and 1.00 A m^{2} respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the result and horizontal magnetic induction at the mid - point O of the line joining their centers is close to (Horizontal component of earth’s magnetic induction is 3.6\times 1 0^{-5} Wb/ m^{2})$ (1) $3.6 \times 1 0^{-5} Wb/ m^{2}$ (2) $2.56 \times 1 0^{-4} Wb/ m^{2}$ (3) $3.50 \times 1 0^{-4} Wb/ m^{2}$ (4) $5.80 \times 1 0^{-4} Wb/ m^{2}$ 535. $An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. (A) The electron will experience magnetic force along the axis of the solenoid. (B) The electron will not experience magnetic force. (C) The electron will continue to move along the axis of the solenoid. (D) The electron will be accelerated along the axis of the solenoid (E) The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the option given below:$ (1) $B, C and D only$ (2) $A and D only$ (3) $B and C only$ (4) $B and E only$ 536. $An electron, moving along the x -axis with an initial energy of 100 eV, enters a region of magnetic field B = (1.5 \times 10^{- 3} T) k at S (see figure). The field extends between x = 0 and x = 2 cm The electron is detected at the point Q on a screen placed 8 cm away from the point S . The distance d between P and Q (on the screen) is:(Electron's charge = 1.6 \times 10^{- 19} C mass of electron (= 9.1 \times 10^{- 31} kg)$ (1) $11.65 cm$ (2) $12.87 cm$ (3) $1.22 cm$ (4) $2.25 cm$ 537. $The magnetic moment of a diamagnetic atom is$ (1) $much greater than one$ (2) $1$ (3) $between zero and one$ (4) $equal to zero$ 538. $A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be x/130 N. The value of x is .$ 539. $Two circular coils P and Q of 100 turns each have same radius of π cm. The currents in P and Q are 1 A and 2 A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is x mT, where x = ____ [Use μ_{0} = 4 π \times 1 0^{- 7} TmA^{- 1}]$ 540. $In the given circuit of potentiometer, the potentital difference E across AB (10 m length) is larger than E_{1} and E_{2} as well. For key K_{1} (closed), the jockey is adjusted to touch the wire at point J_{1} so that there is no deflection in the galvanometer. Now the first battery (E_{1}) is replaced by second battery (E_{2}) for working by making K_{1} open and E_{2} closed. The galvanometer gives then null deflection at J_{2} . The value of \frac{E _{1}}{E _{2}} is \frac{a}{b},, where a =$