Moving Charges & Magnetism PYQs Set 16 (PDF)

Set 16 of 19 · Questions 451-480 of 549

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Mere Teacher · Previous Year Questions JEE Main Physics · Moving Charges & Magnetism · Set 16 (Q451-480)
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451. $Figure shows two semicircular loops of radii R_{1} and R_{2} carrying current t . The magnetic field at the common centre ' O' is$ (1) $\frac{μ _{0} I}{4} (\frac{1}{R _{1}} + \frac{1}{R _{2}})$ (2) $\frac{μ _{0} l}{4} (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ (3) $\frac{μ _{0} I}{2 π} (\frac{1}{R _{1}} + \frac{1}{R _{2}})$ (4) $\frac{μ _{0} I}{2 π} (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ 452. $A and B are two infinitely long straight parallel conductors. C is another straight conductor of length 1 m kept parallel to A and B as shown in the figure. Then the force experienced by C is$ (1) $towards A equal to 0.6\times 1 0^{- 5} N$ (2) $towards B equal to 5.4\times 1 0^{- 5} N$ (3) $towards A equal to 5.4\times 1 0^{- 5} N$ (4) $towards B equal to 0.6\times 1 0^{- 5} N.$ 453. $A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its center will be$ (1) $B \propto r^{2}$ (2) $B \propto r$ (3) $B \propto \frac{1}{r ^{2}}$ (4) $B \propto \frac{1}{r}$ 454. $A cylindrical conductor of radius R is carrying constant current. The plot of the magnitude of the magnetic field, B with the distance, d from the center of the conductor, is correctly represented by the figure:$ (1) (2) (3) (4) 455. $Two tangent galvanometers A and B have coils of radii 8 cm and 16 cm respectively and resistance 8Ω each. They are connected in parallel with a cell of emf 4 V and negligible internal resistance. The deflections produced in the T.G's A and B are 30^{\circ} and 60^{\circ} respectively. If A has 2 turns, then B must have$ (1) $18 turns$ (2) $12 turns$ (3) $6 turns$ (4) $2 turns.$ 456. $A square loop of side 2 a, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0),(b>>a). The magnitude of the torque on the loop about z-axis is given by$ (1) $\frac{2 μ _{0} I ^{2} a ^{2}}{πb}$ (2) $\frac{μ _{0} I ^{2} a ^{2}}{2 πb}$ (3) $\frac{μ _{0} I ^{2} a ^{3}}{2 π b ^{2}}$ (4) $\frac{2 μ _{0} I ^{2} a ^{3}}{π b ^{2}}$ 457. $The figure shows a region of length ’ I ’ with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 \times 10^{5} ms^{- 1} making an angle 60^{\circ} with the field. If the proton completes 10 revolution by the time it cross the region shown ’ l ’, is close to (mass of proton = 1.67 \times 10^{- 27} kg, charge of the proton = 1.6 \times 10^{- 19} C)$ (1) $0.22 m$ (2) $0.11 m$ (3) $0.88 m$ (4) $0.44 m$ 458. $When a proton is released from rest in a room, it starts with an initial acceleration a_{0} towards west. When it is projected towards north with a speed v_{0} it moves with an initial acceleration 3 a_{0} toward west. The electric and magnetic fields in the room are:$ (1) $\frac{m a _{0}}{e} west, \frac{2 m a _{0}}{e v _{0}} down$ (2) $\frac{m a _{0}}{e} east, \frac{3 m a _{0}}{e v _{0}} up$ (3) $\frac{m a _{0}}{e} east, \frac{3 m a _{0}}{e v _{0}} down$ (4) $\frac{m a _{0}}{e} west, \frac{2 m a _{0}}{e v _{0}} up$ 459. $A steady current l flows through a wire with one end at O and the other and extending upto infinity as shwon in the figure. The magnetic field at a point P, located at a distance d from O is$ (1) $\frac{μ _{0} l}{4 π dcos α} (1 - sin α)$ (2) $\frac{μ _{0} l}{2 πdcos α} (1 - sin α)$ (3) $\frac{μ _{0} l}{4 πd}$ (4) $\frac{μ _{0} l}{4 πdsin α} (1 - cos α)$ 460. $A current of 1 A is flowing along the sides of an equilateral triangle of side 4.5 \times 10^{- 2} m . The magnetic field at the centroid of the triangle is (μ_{0} = 4 π \times 10^{- 7} H / m)$ (1) $4 \times 10^{- 5} T$ (2) $2 \times 10^{- 5} T$ (3) $4 \times 10^{- 4} T$ (4) $2 \times 10^{- 4} T$ 461. $A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40 πrad s^{- 1} about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 \times 10^{- 9} T then the charge carried by the ring is close to (μ_{0} = 4 π \times 10^{- 7} N / A^{2}) .$ (1) $2 \times 10^{- 6} C$ (2) $3 \times 10^{- 5} C$ (3) $4 \times 10^{- 5} C$ (4) $7 \times 10^{- 6} C$ 462. $An isosceles triangular current carrying loop is kept perpendicularly in a uniform magnetic field B_{0} as shown in figure. The force on the loop due to magnetic field is$ (1) $I L B_{0} cosθ$ (2) $2 I L B_{0} cosθ$ (3) $0$ (4) $I L B_{0} sin θ$ 463. $One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop (B_{1}) to that at the centre of the coil (B_{C}), i . e, \frac{B _{L}}{B _{C}} will be$ (1) $N$ (2) $\frac{1}{N}$ (3) $N^{2}$ (4) $1/ N^{2}$ 464. $Two infinitely long wires each carrying the same current and pointing in + y direction are placed in the xy -plane, at x = - 2 cm and x = 1 cm . An electron is fired with speed U from the origin making an angle of + 45^{\circ} from the x -axis. The force on the electron at the instant it is fired is (B_{o}) is the magnitude of the field at origin due to the wire at x = 1 cm alone].$ (1) $\frac{- eUB _{o}}{2 2} (i - j)$ (2) $\frac{- eU B _{o}}{2} (i - j)$ (3) $\frac{- e ^{2} B _{o}}{2} (i - j)$ (4) $- eUB_{0} (ı - ȷ)$ 465. $A metallic rod of mass per unit length 0.5 kg m^{-1} is lying horizontally on a smooth inclined plane which makes an angle of 30º with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is:$ (1) $7.14 A$ (2) $11.32 A$ (3) $14.76 A$ (4) $5.98 A$ 466. $Two concentric coils each of radius equal to 2 πcm are placed right angles to each other. If 3 A and 4 A are the currents flowing through the two coils respectively. The magnetic induction (in Wbm^{- 2}) at the centre of the coils will be$ (1) $10^{- 5}$ (2) $7\times 1 0^{- 5}$ (3) $12\times 1 0^{- 5}$ (4) $5\times 1 0^{- 5}$ 467. $Two concentric coils of 20 turns each are placed in same place. Their radii are 30 cm and 60 cm and carry 0.4 A and 0.6 A currents respectively in opposite directions. The magnetic induction at the centre in tesla is \dots \dots ..$ (1) $\frac{8}{3} μ_{0}$ (2) $\frac{2}{3} μ_{0}$ (3) $\frac{5}{3} μ_{0}$ (4) $\frac{10}{3} μ_{0}$ 468. $Two concentric circular loops of radii r_{1} = 30 cm and r_{2} = 50 cm are placed in X-Y plane as shown in the figure. A current I = 7A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately:$ (1) $\frac{7}{2} k A m^{2}$ (2) $- \frac{7}{2} k A m^{2}$ (3) $7 k A m^{2}$ (4) $- 7 k A m^{2}$ 469. $A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength I is passed through the coil, the magnetic field at its centre is$ (1) $\frac{μ _{0} nI}{( b - a )} log_{e} \frac{a}{b}$ (2) $\frac{μ _{0} nI}{2 ( b - a )}$ (3) $\frac{2 μ _{0} nI}{b}$ (4) $\frac{μ _{0} n}{2 ( b - a )} log_{e} \frac{b}{a}$ 470. $A toroid with thick windings of N turns has inner and outer radii R_{1} and R_{2} respectively. If it carries certain steady current I, the variation of the magnetic field due to the toroid with radial distance is correctly graphed in$ (1) (2) (3) (4) 471. $A closely wound solenoid of 2000 turns and area of cross-section 1.5 \times 10^{- 4} m^{2} carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 \times 10^{- 2} tesla making an angle of 30^{\circ} with the axis of the solenoid. The torque on the solenoid will be$ (1) $3 \times 10^{- 3} N m$ (2) $1.5 \times 10^{- 3} N m$ (3) $1.5 \times 10^{- 2} N m$ (4) $3 \times 10^{- 2} N m$ 472. $Two equal electric currents are flowing perpendicular to each other as shown in the figure. AB and CD are perpendicular to each other and symmetrically placed with respect to the currents. Where do we expect the resultant magnetic field to be zero?$ (1) $On CD$ (2) $On AB$ (3) $On both OD and BO$ (4) $On both AB and CD$ 473. $A rectangular coil (Dimension 5 cm \times 2.5 cm with 100 turns, carrying a current of 3 A in the clock-wise direction, is kept centered at the origin and in the X - Z plane. A magnetic field of 1 T is applied along X -axis. If the coil is tilted through 45^{\circ} about Z -axis, then the torque on the coil is:$ (1) $0.38 Nm$ (2) $0.55 Nm$ (3) $0.42 Nm$ (4) $0.27 Nm$ 474. $Nickel shows ferromagnetic property at room temperature. If the temperature is increased beyond Curie temperature, then it will show$ (1) $anti ferromagnetism$ (2) $no magnetic property$ (3) $diamagnetism$ (4) $paramagnetism.$ 475. $In the diagram, I_{1}, I_{2} are the strength of the currents in the loop and straight conductors respectively. OA = OB = R . The net magnetic field at the centre O is zero.Then the ratio of the currents in the loop and the straight conductors is$ (1) $π$ (2) $2 π$ (3) $1/ π$ (4) $1/2 π$ 476. $A moving coil galvanometer of resistance 100Ω is used as an ammeter using a resistance 0.1Ω . The maximum deflection current in the galvanometer is 100 μA . Find the minimum current in the circuit, so that ammeter shows maximum deflection?$ (1) $100.1 mA$ (2) $1000.1 mA$ (3) $10.01 mA$ (4) $1.01 mA$ 477. $Two long wires with no contact are placed perpendicular to each other, i_{1} and i_{2} are currents flowing through these wires, respectively. The magnetic force on a small length dl of the second wire situated at a distance l from first wire is proportional to$ (1) $i_{1} i_{2}$ (2) $i$ (3) $\frac{1}{i _{1} i _{2}}$ (4) $i^{2}$ 478. $A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 \times 1 0^{- 5} T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2. The maximum value of EMF induced (in µV) in the coil will be close to the integer$ 479. $The magnetic field existing in a region is given by B = 0.2 (1 + 2 x) k T . A square loop of edge 50 cm carrying 0.5 A current is placed in x - y plane with its edges parallel to the x - y axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is_____mN .$ 480. $A coil in the shape of an equilateral triangle of side 10cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20mT. The torque acting on the coil when a current of 0.2A is passed through it and its plane becomes parallel to the magnetic field will be x \times 1 0^{- 5} Nm . The value of x is.$