Title 04.Moving Charges and Magnetism.pdf ✅

https://www.chemcontent.com/ 1 4.MOVING CHARGES AND MAGNETISM Physics Smart Booklet Theory + NCERT MCQs + Topic Wise Practice MCQs + NEET PYQs
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https://www.chemcontent.com/ 3 MOVING CHARGES AND MAGNETISM Introduction A gravitational field is associated with a mass. An electrostatic field is associated with a charge. A magnetic field is in a region surrounding a current carrying conductor. • causes affects An electric charge an electricfield an electri ⎯⎯⎯⎯→ ⎯⎯⎯⎯→ c charge • ( ) causes affects electric current A moving electric charge a magnetic fiel ⎯⎯⎯⎯→ ⎯⎯⎯⎯→ d a moving electric charge Magnetic force on a charged particle moving in a magnetic field The force exerted by a magnetic field on a moving electric charge or a current carrying conductor is called magnetic force. A charge q moving with a velocity v  , in a magnetic field B  , experiences a force F  . It is given by F  = q v B    . • The magnitude of the magnetic force is F = q vB sin , where  is the angle between v and B   . • The direction of F  is that of v B    . • F is zero, when v  is parallel or anti parallel to B  ( = 0 or 180). • F is maximum when a charged particle moves in a direction perpendicular to the direction of B  ( = 90). Fmax = q VB sin 90 = q vB. • The work by the magnetic force on a charged particle is zero since F  is perpendicular to v  . Thus, a magnetic field cannot change the speed and kinetic energy of a charged particle. Fleming’s left hand rule The direction of the force on a charged particle moving perpendicular to a magnetic field is given by Fleming’s left hand rule. Stretch the first three fingers of the left hand such that they are mutually perpendicular. If the forefinger is in the direction of the field, the middle finger in the direction of velocity of the positively charged particle then the thumb gives the direction of the mechanical force. Motion of a charged particle with v  perpendicular to B  Consider a positively charged particle moving in a uniform magnetic field. When the initial velocity of the particle is perpendicular to the field, (in the figure, the magnetic field is perpendicular to the plane of the paper and inwards) the particle moves in a circular path whose plane is perpendicular to the magnetic field. Thus, the centripetal force r mv2 is provided by the magnetic force qvB, where r = radius of the circular path.  r = qB mv . The angular speed of the particle,  = m qB r v = . The period of circular motion, T = qB 2 2 m v 2 r  =   =  and frequency qB f 2 m =  Thus, the angular speed of the particle, period of the circular motion and frequencies of rotation do not depend on the translational speed of the particle or the radius of the orbit, for a given charged particle in a given uniform magnetic field. This principle is used in the design of a particle accelerator called cyclotron. Force Velocity Field Fleming’s left hand rule  Force on a moving charge    Bin +q +q FB FB +q F r   
https://www.chemcontent.com/ 4 Cyclotron Cyclotron is a device used to accelerate charged particles to very large kinetic energies by applying electric and magnetic fields. (a) (b) Schematic diagram of cyclotron • Expression for kinetic energy The maximum kinetic energy, of the ion as it emerges from the cyclotron will then be 2 2 2 max max B q R (Kinetic energy) , K 2m =  2 max q K . m  • Cyclotron frequency The frequency f, of the oscillator required to keep the ion in phase is the reciprocal of the time in which the particle makes one revolution. This is called the cyclotron frequency given by Bq f 2 m =  It can be shown that kinetic energy = 2m 2 f 2R 2 Helical path of a charged particle moving in a magnetic field (0 <  <90°) • If a charged particle moves in a uniform magnetic field with its velocity at some arbitrary angle  (0 <  < 90) with respect to a magnetic field B  , the path is a helix. • The axis of the helix is along the direction of B. • The perpendicular component of velocity (v sin ) determines the radius (r) of the helix. Then, qB mv sin r  = • The pitch of the helix p (vcos )T, =  where T is the period of the circular motion and is given by 2 m T qB  = The Pitch of the helical path (p) is the distance travelled by the particle along the direction of the field in one period of revolution of the circular motion.  2 m v cos p qB   =