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CBSE Class 12th Physics Notes: Moving Charges and Magnetism (Part ‒ I)

Nov 25, 2016 14:00 IST

    Chapter-wise revision notes on Chapter-4: Moving Charges and Magnetism of NCERT class 12 Physics textbook is available here.

    Moving Charges and Magnetism is one of the important chapters of CBSE class 12 Physics. So, students must prepare this chapter thoroughly. The notes provided here will be very helpful for the students who are going to appear in CBSE class 12 Physics board exam 2017. The notes of this chapter are available in several parts. This is part I of the chapter.

    The topics covered in this part are given below:

         • Oersted’ Experiment

         • Magnetic Field

         • Moving Charge & Magnetic Field

         • Lorentz Force

         • Magnetic force on a current-carrying conductor

         • Motion of a charged particle in a Magnetic Field

         • Motion of a charge in Combined Electric and Magnetic Fields

         • Cyclotron

    Oersted’ Experiment

    During a lecture demonstration in 1820, the Danish physicist Hans Christian Oersted noticed that a current in a straight wire caused a noticeable deflection in a nearby magnetic compass needle. He further investigated this phenomenon and confirmed the phenomenon of magnetic field around current carrying conductor.

    CBSE Class 12 Physics Syllabus: 2017

    Magnetic Field

    It is the space around a magnet or current carrying conductor around which magnetic effects can be experienced. It is a vector quantity and its SI unit is tesla (T) or Wbm‒2.

    Moving Charge & Magnetic Field

    A charge can produce magnetic field if it is in motion. Magnetic field can also interact with a moving charge.

    Lorentz Force

    Assume a point charge q (moving with a velocity v and, located at r at a given time t) in presence of both the electric field E (r) and the magnetic field B (r). The force on an electric charge q due to both of them is given by,

    F = q [E (r) + v × B (r)] ≡ FElectric + FMagnetic

    Careful analysis of this expression shows that:

    •     Lorentz Force depends on q, v and B (charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge.

    •     The magnetic force q [v × B] includes a vector product of velocity & magnetic field. Vector product makes the force due to magnetic field become zero if velocity and magnetic field are parallel or anti-parallel. The force acts in a (sideways) direction perpendicular to both the velocity and the magnetic field. Its direction is given by the screw rule or right hand rule for vector (or cross) product as shown in figure given below

    Direction of magnetic field by right hand rule for vector

    Image Source: NCERT Books

    •     The magnetic force is zero if charge is not moving (as then |v|= 0). Only a moving charge feels the magnetic force

    F = q [v × B] =q |v||B| sin θ ň, where θ is angle between v and B.

    CBSE Class 12th Physics Notes: Wave Optics

    Magnetic force on a current-carrying conductor

    Magnetic force on a conductor of length l carrying a current I placed in a uniform magnetic field B is given by

    F = I (l × B) or |F| = I |l|| B| sin θ.

    The direction of F is perpendicular to both l and B and can be obtained with the help of Fleming’s Left hand rule.

    Motion of a charged particle in Magnetic Field

    A force on a particle does work if the force has a component along (or opposed to) the direction of motion of the particle.

    In the case of motion of a charge in a magnetic field, the magnetic force is perpendicular to the velocity of the particle. So no work is done and no change in the magnitude of the velocity is produced (though the direction of momentum may be changed).

    Generally two types of cases are possible:

    Case 1st: When v is perpendicular to B

    The perpendicular force, q v × B, acts as a centripetal force and produces a circular motion perpendicular to the magnetic field. The particle will describe a circle if v and B are perpendicular to each other.

    Charge particle describing a circle if v and B are mutually perpendicular

    Image Source: NCERT Books

    In this case, radius described by charge particle is given by, r = m v / q B

    If ω is the angular frequency, then ω = 2πv = q B / m, where, v is frequency of rotation

    The time taken for one revolution is T= 2π/ω ≡ 1/ν.

    Case 2nd: When v is making an angle with B other than 0o

    In this case, velocity has a component along B, this component remains unchanged as the motion along the magnetic field will not be affected by the magnetic field. The motion in a plane perpendicular to B is as before a circular one, thereby producing a helical motion

    Helical Path of a moving charge particle in magnetic field

    Image Source: NCERT Books

    The distance moved along the magnetic field in one rotation is called pitch p and,

    p = v||T = 2πm v|| / q B

    The radius of the circular component of motion is called the radius of the helix.

    CBSE Class 12th Physics Notes: Ray Optics & Optical Instruments

    Motion of a charge in Combined Electric and Magnetic Fields

    A charge q moving with velocity v in presence of both electric and magnetic fields experiences a force given by F = q (E + v × B) = FE + FB

    Motion of a charge in Cross Electric and Magnetic Fields

    Image Source: NCERT Books

    Consider the situation shown in figure given above, in this particular case we have:

    Force on charge particle in cross electric and magnetic fields

    Here, electric and magnetic forces are in opposite directions as shown in the figure.

    If we adjust the value of E and B such that magnitude of the two forces are equal. Then, total force on the charge is zero and the charge will move in the fields undeflected.

    This happens when, qE = qvB or v = E/B

    This condition can be used to select charged particles of a particular velocity out of a beam containing charges moving with different speeds (irrespective of their charge and mass). The crossed E and B fields, therefore, serve as a velocity selector.

    Only particles with speed E/B pass undeflected through the region of crossed fields.

    CBSE Class 12th Physics Notes: Semiconductor Electronics

    Cyclotron:

    It is a machine to accelerate charged particles or ions to high energies.

    The cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles. As the fields are perpendicular to each other they are called crossed fields.

    Construction of Cyclotron

    Image Source: NCERT Books

    A schematic sketch of the cyclotron is shown in the figure given above. There is a source of charged particles or ions at P which move in a circular fashion in the dees, D1 and D2, on account of a uniform perpendicular magnetic field B. An alternating voltage source accelerates these ions to high speeds. The ions are eventually ‘extracted’ at the exit port.

    In case of cyclotron,

    cyclotron frequency and maximum kinetic energy

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