Title 04. MOVING CHARGES AND MAGNETISM (1).pdf ✅

Moving Charges and Magnetism 4.2 Magnetic Force 1. A wire carrying a current I along the positive x- axis has length L. It is kept in a magnetic field B⃗ = (2iˆ + 3jˆ − 4kˆ )T. The magnitude of the magnetic force acting on the wire is (a) 5IL (b) √3IL (c) 3IL (d) √5IL (2023) 2. In the product F = q(v × B⃗ ) = qv × (Biˆ + Bjˆ + B0kˆ ) For q = 1 and v = 2iˆ + 4jˆ + 6kˆ and F = 4iˆ − 20jˆ + 12kˆ What will be the complete expression for B⃗ ? (a) 6iˆ + 6jˆ − 8kˆ (b) −8iˆ − 8jˆ − 6kˆ (c) −6iˆ − 6jˆ − 8kˆ (d) 8iˆ + 8jˆ − 6kˆ (2021) 3. 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 30∘ 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 (a) 7.14 A (b) 5.98 A (c) 14.76 A (d) 11.32 A (2018) 4. When a proton is released from rest in a room, it starts with an initial acceleration a0 towards west. When it is projected towards north with a speed v0 it moves with an initial acceleration 3a0 toward west. The electric and magnetic fields in the room are (a) ma0 e east, 3ma0 ev0 up (b) ma0 e east, 3ma0 ev0 down (c) ma0 e west, 2ma0 ev0 up (d) ma0 e west, 2ma0 ev0 down (2013) 5. A long straight wire carries a certain current and produces a magnetic field 2 × 10−4 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 107 m/s towards the wire along perpendicular to it. The force experienced by the electron will be (charge on electron 1.6 × 10−19C ) (a) 3.2 N (b) 3.2 × 10−16 N (c) 1.6 × 10−16 N (d) zero (Karnataka NEET 2013) 6. A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron (a) will turn towards right of direction of motion (b) speed will decrease (c) speed will increase (d) will turn towards left of direction of motion. (2011) 7. The magnetic force acting on a charged particle of charge −2μC in a magnetic field of 2 T acting in y direction, when the particle velocity is (2iˆ + 3jˆ) × 106 m s −1 is (a) 4 N in z direction (b) 8 N in y direction (c) 8 N in z direction (d) 8 N in −z direction (2009) 8. When a charged particle moving with velocity v is subjected to a magnetic field of induction B⃗ , the force on it is non-zero. This implies that (a) angle between is either zero or 180∘ (b) angle between is necessarily 90∘ (c) angle between can have any value other than 90∘ (d) angle between can have any value other than zero and 180∘ . (2006)
9. A very long straight wire carries a current I. At the instant when a charge +Q at point P has velocity v , as shown, the force on the charge is (a) along Oy (b) Opositte to Oy (c) along Ox (d) opposite to Ox. 10. A charge q moves in a region where electric field and magnetic field both exist, then force on it is (a) q(v × B⃗ ) (b) qE⃗ + q ̇ (v × B⃗ ) (c) qE⃗ + q (B⃗ × v ) (d) qB⃗ + q(E⃗ × v ) (2002) 11. Tesla is the unit of (a) electric field (b) magnetic field (c) electric flux (d) magnetic flux (1997,1988) 12. A charge moving with velocity v in X-direction is subjected to a field of magnetic induction in negative X-direction. As a result, the charge will (a) remain unaffected (b) start moving in a circular path Y-Z plane (c) retard along X-axis (d) moving along a helical path around X-axis. (1993) 13. A straight wire of length 0.5 metre 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 (a) 2.4 N (b) 1.2 N (c) 3.0 N (d) 2.0 N . (1992) 4.3 Motion in a Magnetic Field 14. Ionized hydrogen atoms and α-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths rH: rα will be (a) 1: 4 (b) 2: 1 (c) 1: 2 (d) 4: 1 (2019) 15. A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV , the energy acquired by the alpha particle will be (a) 1.5 MeV (b) 1 MeV (c) 4 MeV (d) 0.5 MeV (2015) 16. A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an α-particle to describe a circle of same radius in the same field? (a) 2 MeV (b) 1 MeV (c) 0.5 MeV (d) 4 MeV (Mains 2012) 17. Under the influence of a uniform magnetic field, a charged particle moves with a constant speed v in a circle of radius R. The time period of rotation of the particle (a) depends on R and not on v (b) is independent of both v and R (c) depends on both v and R (d) depends on v and not on R. (2009, 2007) 18. A particle of mass m, charge Q and kinetic energy T enters in a transverse uniform magnetic field of induction B⃗ . After 3 seconds the kinetic energy of the particle will be (a) T (b) 4T (c) 3T (d) 2T (2008)

E⃗ should be perpendicular to the direction of velocity Which one of the following pairs of statements is possible? (a) (1) and (3) (b) (3) and (4) (c) (2) and (3) (d) (2) and (4) (Mains 2010) 28. A beam of electron passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move (a) in a circular orbit (b) along a parabolic path (c) along a straight line (d) in an elliptical orbit. (2007) 29. In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio ( charge on the ion mass of the ion ) will be proportional to (a) 1/R 2 (b) R 2 (c) R (d) 1/R (2007) 30. In Thomson mass spectrograph E⃗ ⊥ B⃗ then the velocity of electron beam will be (a) |E⃗ | |B⃗ | (b) E⃗ × B⃗ (c) |B⃗ | |E⃗ | (d) E 2 B2 (2001) 31. A beam of electrons is moving with constant velocity in a region having electric and magnetic fields of strength 20 V m−1 and 0.5 T at right angles to the direction of motion of the electrons. What is the velocity of the electrons? (a) 8 m s −1 (b) 5.5 m s −1 (c) 20 m s −1 (d) 40 m s −1 (1996) 4.4 Magnetic Field due to a Current Element, Biot-Savart Law 32. 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. (a) Both Statement I and Statement II are correct. (b) Both Statement I and Statement II are incorrect. (c) Statement I is correct and Statement II is incorrect. (d) Statement I is incorrect and Statement II is correct. (2022) 33. The magnetic field dB⃗ due to a small current element dl at a distance r and element carrying current i is (a) dB⃗ = μ0 4π i 2 ( dl ×r r ) (b) dB⃗ = μ0 4π i ( dl ×r r 3 ) (c) dB⃗ = μ0 4π i ( dl ×r r ) (d) dB⃗ = μ0 4π i 2 ( dl ×r r 2 ) (1996) 4.5 Magnetic Field on the Axis of a Circular Current Loop 34. Averylong conducting wire is bent in a semi- circular shape from A to B as shown in figure. The magnetic field at point P for steady current