Moving Charges & Magnetism PYQs Set 14 (PDF)

Set 14 of 19 · Questions 391-420 of 549

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Mere Teacher · Previous Year Questions JEE Main Physics · Moving Charges & Magnetism · Set 14 (Q391-420)
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391. $The magnetic field at the center ' O' in the given figure is$ (1) $\frac{3}{10} \frac{μ _{0} I}{R}$ (2) $\frac{7}{14} \frac{μ _{0} I}{R}$ (3) $\frac{μ _{0} I}{12 R}$ (4) $\frac{5}{12} \frac{μ _{0} I}{R}$ 392. $Two infinitely long straight wires A and B, each carrying current I are placed on x and y -axis, respectively. The current in wires A and B flow along - i and j directions respectively. The force on a charged particle having charge q, moving from position, r = d (i + j) with velocity v = v i is$ (1) $\frac{μ _{0} Iqv}{2 πd} j$ (2) $\frac{μ _{0} Iqv}{πd} j$ (3) $\frac{μ _{0} Iqv}{2 πd} k$ (4) $0$ 393. $A metal wire is of length l and magnetic moment M . What is the new magnetic moment if it is bent in L -shape?$ (1) $2 M$ (2) $\frac{M}{2}$ (3) $M$ (4) $\frac{M}{2}$ 394. $The ratio of heats generated through shunt and galvanometer is 7 : 5 when they are connected to make an ammeter. If the resistance of the galvanometer is 112Ω then the resistance of the shunt is$ (1) $80Ω$ (2) $8Ω$ (3) $15.6Ω$ (4) $1.56Ω$ 395. $A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A . The magnetic field at point O will be close to:$ (1) $1.0 \times 10^{- 7} T$ (2) $1.5 \times 10^{- 7} T$ (3) $1.5 \times 10^{- 5} T$ (4) $1.0 \times 10^{- 5} T$ 396. $A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2m/s. The angle of the deviation (θ) of the path of the electron as it comes out of the field will be _______$ (1) $t a n^{- 1} (4)$ (2) $t a n^{- 1} (2)$ (3) $t a n^{- 1} (\frac{1}{3})$ (4) $t a n^{- 1} (3)$ 397. $The magnetic induction at point O of the given infinitely long current carrying wire shown in the figure below is$ (1) $\frac{μ _{0} l}{4 πR} (1 - \frac{3 π}{2})$ (2) $\frac{μ _{0} l}{2 R ( 1 + π )}$ (3) $\frac{μ _{0} l}{4 πR} (1 + \frac{3 π}{2})$ (4) $\frac{μ _{0} l}{4 πR}$ 398. $A thin circular disk of radius R is uniformly charged with density σ > 0 per unit area. The disk rotates about its axis with a uniform angular speed ω . The magnetic moment of the disk is:$ (1) $π R^{4} σω$ (2) $\frac{π R ^{4}}{2} σω$ (3) $\frac{π R ^{4}}{4} σω$ (4) $2 π R^{4} σω$ 399. $A positively charged particle of mass m is passed through a velocity selector. It moves horizontally rightward without deviation along the line y = \frac{2 mv}{qB} with a speed v . The electric field is vertically downward and magnetic field is into the plane of the paper. Now, the electric field is switched off at t = 0 . The angular momentum of the charged particle about the origin O at t = \frac{πm}{qB} is$ (1) $\frac{m E ^{2}}{q B ^{3}}$ (2) $\frac{2 m E ^{2}}{q B ^{3}}$ (3) $zero$ (4) $\frac{4 m ^{2} E ^{2}}{q B ^{3}}$ 400. $Figure shows a current carrying square loop ABCD of edge length is ' a' lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2 r, then the magnitude of the resultant magnetic field at centre of the square loop is$ (1) $\frac{2 μ _{0} I}{3 πa}$ (2) $\frac{2 μ _{0} I}{3 πa}$ (3) $\frac{3 π μ _{0} I}{2 a}$ (4) $\frac{μ _{0} I}{2 πa}$ 401. $There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1:1. The magnetic field at point P is$ (1) $\frac{μ _{0} I}{4 πxy} (x^{2} + y^{2} + (x + y))$ (2) $\frac{μ _{0} I}{4 πxy} (x^{2} + y^{2} - (x + y))$ (3) $\frac{μ _{0} Ixy}{4 π} (x^{2} + y^{2} - (x + y))$ (4) $\frac{μ _{0} Ixy}{4 π} (x^{2} + y^{2} + (x + y))$ 402. $Two wires A & B are carrying currents I_{1} and I_{2} as shown in the figure. The separation between them is d . A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are:$ (1) $x = (\frac{I _{1}}{I _{1} - I _{2}}) d and x = \frac{I _{2}}{( I _{1} + I _{2} )} d$ (2) $x = (\frac{I _{2}}{( I _{1} + I _{2} )}) d and x = (\frac{I _{2}}{( I _{1} - I _{2} )}) d$ (3) $x = (\frac{I _{1}}{( I _{1} + I _{2} )}) d and x = (\frac{I _{2}}{( I _{1} - I _{2} )}) d$ (4) $x = \pm \frac{I _{1} d}{( I _{1} - I _{2} )}$ 403. $At a point A on the earth’s surface of angle of dip, d = +25º. At a point B on the earth’s surface the angle of dip, d = -25º. We can interpret that:$ (1) $A and B are both located in the southern hemisphere.$ (2) $A and B are both located in the northern hemisphere.$ (3) $A is located in the southern hemisphere and B is located in the northern hemisphere.$ (4) $A is located in the northern hemisphere and B is located in the southern hemisphere.$ 404. $A long straight wire carries a certain current and produces a magnetic field 2 \times 1 0^{- 4} Wb m^{- 2} at a perpendicular distance of 5 cm from the wire. An electron situated at 5 cm from the wire moves with a velocity 1 0^{7} m / s towards the wire along perpendicular to it. The force experienced by the electron will be (charge on electron 1.6 \times 1 0^{- 19} C)$ (1) $3.2 N$ (2) $3.2 \times 1 0^{- 16} N$ (3) $1.6 \times 1 0^{- 16} N$ (4) $zero.$ 405. $What is the value of shunt resistance required to convert a galvanometer of resistance 100Ω into an ammeter of range 1 A ? Given: Full scale deflection of the galvanometer is 5 mA .$ (1) $0.5Ω$ (2) $\frac{5}{9.95} Ω$ (3) $0.05Ω$ (4) $\frac{9.95}{5} Ω$ 406. $A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Wb / m^{2} . The coil carries a current of 2 A. If the plane of the coil is inclined at an angle of 30^{\circ} with the direction of the field. the torque required to keep the coil in stable equilibrium will be$ (1) $0.15 N - m$ (2) $0.20 N - m$ (3) $0.24 N - m$ (4) $0.12 N - m$ 407. $Two long parallel straight metal wires A and B carrying currents 12 A and 36 A respectively, in the same direction are separated by 50 cm . The point relative to A, where the resultant magnetic induction between the two wires due to the currents is zero, will be$ (1) $90 cm$ (2) $7.5 cm$ (3) $28 cm$ (4) $12.5 cm$ 408. $A long straight wire carrying a current of 25 A rests on the table. Another wire PQ of length 1 m and mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will wire PQ rise? (μ_{0} = 4 π \times 10^{- 7} SI unit)$ (1) $3 mm$ (2) $4 mm$ (3) $5 mm$ (4) $8 mm$ 409. $Three parallel wires a, b and c carrying currents i_{a}, i_{b} and i_{c} as shown in the figure are placed next to each other. The magnitude force on a length l of the wire a, if d_{2} = 2 d_{1}, i_{b} = i_{a} and i_{c} = 4 i_{a} is$ (1) $\frac{μ _{0}}{6 π d _{1}} i_{a}^{2} l$ (2) $\frac{μ _{0}}{2 π d _{1}} i_{a}^{2} l$ (3) $\frac{μ _{0}}{4 π d _{1}} i_{a}^{2} l$ (4) $\frac{μ _{0}}{3 π d _{1}} i_{a}^{2} l$ 410. $A current I a flows in a circular arc of radius r subtending an angle θ as shown in the figure. Find the magnetic field at the centre O of the circle.$ (1) $\frac{μ _{0} Iθ}{4 πr}$ (2) $\frac{2 μ _{0} I \cdot sin θ}{4 πr}$ (3) $\frac{2 μ _{0} Isin θ}{2 r}$ (4) $\frac{2 μ _{0} Isin θ}{4 r}$ 411. $An iron bar of length l has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle 60^{\circ} with each other. The magnetic moment of this new magnet is [NEET 2024]$ (1) $M$ (2) $\frac{M}{2}$ (3) $2M$ (4) $\frac{M}{3}$ 412. $Two tangent galvanometers A and B are identical except in their number of turns. They are connected in series. On passing a current through them, deflections of 60^{\circ} and 30^{\circ} are produced. The ratio of the number of turns in A and B is$ (1) $1 : 2$ (2) $2 : 1$ (3) $1 : 3$ (4) $3 : 1$ 413. $The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity co-ercivity and saturation, respectively, of the material are :$ (1) $50 A / m, 1 T, 1.5 T$ (2) $1.5 T, 50 A / m, 1 T$ (3) $1 T, 50 A / m, 1.5 T$ (4) $50 A / m, 1.5 T, 1 T$ 414. $A very long wire carrying a current 42 A is bent at a right angles. The magnitude of magnetic field (\| B \|) at a point P lying on a line perpendicular to the bent wire at a distance, d = 20 cm from the point of the bending will be (Let μ_{0} = 4 π \times 10^{- 7} H / m)$ (1) $1 μT$ (2) $0.8 μT$ (3) $2 μT$ (4) $4 μT$ 415. $ABCD is a rectangular loop made of uniform wire. If AD = BC = 2 cm, what is the magnetic force per unit length acting on wire DC due to wire AB, if ammeter reads 20 A ? (The length of AB and DC are large in comparison with other two sides)$ (1) $10^{- 1} Nm^{- 1}$ (2) $10^{- 2} Nm^{- 1}$ (3) $10^{- 3} Nm^{- 1}$ (4) $10^{- 4} Nm^{- 1}$ 416. $An electron moves in a circular orbit with a uniform speed v . It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional to$ (1) $B / v$ (2) $B / v$ (3) $v / B$ (4) $vlB$ 417. $Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is x \times 10^{- 5} T . The value of x is . Take permeability of free space as μ_{0} = 4 π \times 10^{- 7} SI units.$ 418. $A square loop of edge length 2 m carrying current of 2 A is placed with its edges parallel to the xy axis. A magnetic field is passing through the x - y plane and expressed as B = B_{0} (1 + 4 x) k, where B_{0} = 5 T . The net magnetic force experienced by the loop is _____N .$ 419. $A loop ABCDEFA of straight edges has six corner points A (0, 0, 0), B (5, 0, 0), C (5, 5, 0), D (0, 5, 0), E (0, 5, 5) and F (0, 0, 5) . The magnetic field in this region is B = (3 i + 4 k) T . The quantity of flux through the loop ABCDEFA (in Wb) is$ 420. $A loop ABCDA, carrying current I = 12 A, is placed in a plane, consists of two semi-circular segments of radius R_{1} = 6 π m and R_{2} = 4 π m . The magnitude of the resultant magnetic field at center O is k \times 10^{- 7} T . The value of k is . (Given (μ_{0} = 4 π \times 10^{- 7} TmA^{- 1})$