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      Class 12 PHYSICS – JEE

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      • Class 12 PHYSICS – JEE
      CoursesClass 12PhysicsClass 12 PHYSICS – JEE
      • 1.Electrostatics (1)
        8
        • Lecture1.1
          Charge, Coulombs Law and Coulombs law in Vector form 41 min
        • Lecture1.2
          Electric Field; Electric Field Lines; Field lines due to multiple charges 42 min
        • Lecture1.3
          Charge Distribution; Finding Electric Field due to Different Object 01 hour
        • Lecture1.4
          Solid angle; Area Vector; Electric Flux; Flux of closed surface; Gauss Law 47 min
        • Lecture1.5
          Finding E Using Concept of Gauss law and Flux 01 hour
        • Lecture1.6
          Chapter Notes – Electrostatics (1)
        • Lecture1.7
          NCERT Solutions – Electrostatics
        • Lecture1.8
          Revision Notes Electrostatics
      • 2.Electrostatics (2)
        7
        • Lecture2.1
          Work done by Electrostatic Force; Work done by man in E-Field; Electrostatic Potential Energy 49 min
        • Lecture2.2
          Finding Electric Potential, Equipotential Surface and Motion in Electric Field 01 hour
        • Lecture2.3
          Electric Dipole and Dipole in Uniform and Non-uniform Electric field 01 hour
        • Lecture2.4
          Analysis of charge on conductors; Potential due to induced charge 58 min
        • Lecture2.5
          Conductors with cavity- Case 1: Empty cavity, Case 2: Charge Inside Cavity 41 min
        • Lecture2.6
          Connecting Two Conductors; Grounding of conductor; Electric field just outside conductor; Electrostatic pressure; Self potential Energy 54 min
        • Lecture2.7
          Chapter Notes – Electrostatics (2)
      • 3.Current Electricity (1)
        9
        • Lecture3.1
          Current, Motion of Electrons in Conductor; Temp. Dependence of Resistor 26 min
        • Lecture3.2
          Circuit Theory and Kirchoffs Laws 31 min
        • Lecture3.3
          Some Special Circuits- Series & Parallel Circuits, Open Circuit, Short Circuit 26 min
        • Lecture3.4
          Wheatstone Bridge, Current Antisymmetric 21 min
        • Lecture3.5
          Equivalent Resistance- Series and parallel, Equipotential Points, Wheatstone Bridge 25 min
        • Lecture3.6
          Current Antisymmetric, Infinite Ladder, Circuit Solving, 3D circuits 20 min
        • Lecture3.7
          Chapter Notes – Current Electricity
        • Lecture3.8
          NCERT Solutions – Current Electricity
        • Lecture3.9
          Revision Notes Current Electricity
      • 4.Current Electricity (2)
        4
        • Lecture4.1
          Heating Effect of Current; Rating of Bulb; Fuse 19 min
        • Lecture4.2
          Battery, Maximum power theorem; Ohmic and Non Ohmic Resistance; Superconductor 31 min
        • Lecture4.3
          Galvanometer; Ammeter & Voltmeter and Their Making 44 min
        • Lecture4.4
          Potentiometer and its applications ; Meter Bridge; Post Office Box; Colour Code of Resistors 32 min
      • 5.Capacitor
        6
        • Lecture5.1
          Capacitor and Capacitance; Energy in Capacitor 38 min
        • Lecture5.2
          Capacitive Circuits- Kirchoff’s Laws; Heat Production 01 hour
        • Lecture5.3
          Equivalent Capacitance; Charge on both sides of cap. Plate 52 min
        • Lecture5.4
          Dielectric Strength; Polar and Non-Polar Dielectric; Equivalent Cap. with Dielectric 01 hour
        • Lecture5.5
          Inserting and Removing Dielectric- Work (Fringing Effect), Force; Force between plates of capacitor 38 min
        • Lecture5.6
          Revision Notes Capacitor
      • 6.RC Circuits
        3
        • Lecture6.1
          Maths Needed for RC Circuits, RC circuits-Charging Circuit 19 min
        • Lecture6.2
          RC circuits-Discharging Circuit, Initial & Steady State, Final (Steady) State, Internal Resistance of Capacitor 44 min
        • Lecture6.3
          Revision Notes RC Circuits
      • 7.Magnetism and Moving Charge
        16
        • Lecture7.1
          Introduction, Vector Product, Force Applied by Magnetic Field, Lorentz Force, Velocity Selector 40 min
        • Lecture7.2
          Motion of Charged Particles in Uniform Magnetic Field 40 min
        • Lecture7.3
          Cases of Motion of Charged Particles in Uniform Magnetic Field 56 min
        • Lecture7.4
          Force on a Current Carrying Wire on Uniform B and its Cases, Questions and Solutions 59 min
        • Lecture7.5
          Magnetic Field on Axis of Circular Loop, Magnetic field due to Moving Charge, Magnetic Field due to Current 52 min
        • Lecture7.6
          Magnetic Field due to Straight Wire, Different Methods 40 min
        • Lecture7.7
          Magnetic Field due to Rotating Ring and Spiral 41 min
        • Lecture7.8
          Force between Two Current Carrying Wires 36 min
        • Lecture7.9
          Force between Two Current Carrying Wires 58 min
        • Lecture7.10
          Miscellaneous Questions 55 min
        • Lecture7.11
          Solenoid, Toroid, Magnetic Dipole, Magnetic Dipole Momentum, Magnetic Field of Dipole 54 min
        • Lecture7.12
          Magnetic Dipole in Uniform Magnetic Field, Moving Coil Galvanometer, Torsional Pendulum 01 hour
        • Lecture7.13
          Advanced Questions, Magnetic Dipole and Angular Momentum 56 min
        • Lecture7.14
          Chapter Notes – Magnetism and Moving Charge
        • Lecture7.15
          NCERT Solutions – Magnetism and Moving Charge
        • Lecture7.16
          Revision Notes Magnetism and Moving Charge
      • 8.Magnetism and Matter
        10
        • Lecture8.1
          Magnetic Dipole, Magnetic Properties of Matter, Diamagnetism; Domain Theory of Ferro 47 min
        • Lecture8.2
          Magnetic Properties of Matter in Detail 39 min
        • Lecture8.3
          Magnetization and Magnetic Intensity, Meissner Effect, Variation of Magnetization with Temperature 55 min
        • Lecture8.4
          Hysteresis, Permanent Magnet, Properties of Ferro for Permanent Magnet, Electromagnet 31 min
        • Lecture8.5
          Magnetic Compass, Earth’s Magnetic Field 20 min
        • Lecture8.6
          Bar Magnet, Bar Magnet in Uniform Field 49 min
        • Lecture8.7
          Magnetic Poles, Magnetic Field Lines, Magnetism and Gauss’s Law 32 min
        • Lecture8.8
          Chapter Notes – Magnetism and Matter
        • Lecture8.9
          NCERT Solutions – Magnetism and Matter
        • Lecture8.10
          Revision Notes Magnetism and Matter
      • 9.Electromagnetic Induction
        14
        • Lecture9.1
          Introduction, Magnetic Flux, Motional EMF 01 min
        • Lecture9.2
          Induced Electric Field, Faraday’s Law, Comparison between Electrostatic Electric Field and Induced Electric Field 43 min
        • Lecture9.3
          Induced Current; Faraday’s Law ; Lenz’s Law 56 min
        • Lecture9.4
          Faraday’s Law and its Cases 50 min
        • Lecture9.5
          Advanced Questions on Faraday’s Law 37 min
        • Lecture9.6
          Cases of Current Electricity 59 min
        • Lecture9.7
          Lenz’s Law and Conservation of Energy, Eddy Current, AC Generator, Motor 01 hour
        • Lecture9.8
          Mutual Induction 53 min
        • Lecture9.9
          Self Inductance, Energy in an Inductor 34 min
        • Lecture9.10
          LR Circuit, Decay Circuit 01 hour
        • Lecture9.11
          Initial and Final Analysis of LR Circuit 38 min
        • Lecture9.12
          Chapter Notes – Electromagnetic Induction
        • Lecture9.13
          NCERT Solutions – Electromagnetic Induction
        • Lecture9.14
          Revision Notes Electromagnetic Induction
      • 10.Alternating Current Circuit
        8
        • Lecture10.1
          Introduction, AC/DC Sources, Basic AC Circuits, Average & RMS Value 46 min
        • Lecture10.2
          Phasor Method, Rotating Vector, Adding Phasors, RC Circuit 35 min
        • Lecture10.3
          Examples and Solutions 21 min
        • Lecture10.4
          Power in AC Circuit, Resonance Frequency, Bandwidth and Quality Factor, Transformer 51 min
        • Lecture10.5
          LC Oscillator, Question and Solutions of LC Oscillator, Damped LC Oscillator 53 min
        • Lecture10.6
          Chapter Notes – Alternating Current Circuit
        • Lecture10.7
          NCERT Solutions – Alternating Current Circuit
        • Lecture10.8
          Revision Notes Alternating Current Circuit
      • 11.Electromagnetic Waves
        4
        • Lecture11.1
          Displacement Current; Ampere Maxwell Law 14 min
        • Lecture11.2
          EM Waves; EM Spectrum; Green House Effect; Ozone Layer 36 min
        • Lecture11.3
          Chapter Notes – Electromagnetic Waves
        • Lecture11.4
          Revision Notes Electromagnetic Waves
      • 12.Photoelectric Effect
        5
        • Lecture12.1
          Recalling Basics; Photoelectric Effect 50 min
        • Lecture12.2
          Photo-electric Cell 35 min
        • Lecture12.3
          Photon Flux; Photon Density; Momentum of Photon; Radiation Pressure- Full Absorption, Full Reflection; Dual nature 52 min
        • Lecture12.4
          Chapter Notes – Photoelectric Effect
        • Lecture12.5
          Revision Notes Photoelectric Effect
      • 13.Ray Optics (Part 1)
        12
        • Lecture13.1
          Rays and Beam of Light, Reflection of Light, Angle of Deviation, Image Formation by Plane Mirror 01 hour
        • Lecture13.2
          Field of View, Numerical on Field of Line, Size of Mirror 42 min
        • Lecture13.3
          Curved Mirrors, Terms Related to Curved Mirror, Reflection of Light by Curved Mirror 40 min
        • Lecture13.4
          Image Formation by Concave Mirror, Magnification or Lateral or Transverse Magnification 01 hour
        • Lecture13.5
          Ray Diagrams for Concave Mirror 45 min
        • Lecture13.6
          Image Formation by Convex Mirror; Derivations of Various Formulae used in Concave Mirror and Convex Mirror 01 hour
        • Lecture13.7
          Advanced Optical Systems, Formation of Images with more than one Mirror 24 min
        • Lecture13.8
          Concept of Virtual Object, Formation of Image when Incident ray are Converging, Image Characteristics for Virtual Object, 55 min
        • Lecture13.9
          Newton’s Formula, Longitudinal Magnification 23 min
        • Lecture13.10
          Formation of Image when Two Plane Mirrors kept at an angle and parallel; Formation of Image by two Parallel Mirrors. 43 min
        • Lecture13.11
          Chapter Notes – Ray Optics
        • Lecture13.12
          NCERT Solutions – Ray Optics
      • 14.Ray Optics (Part 2)
        13
        • Lecture14.1
          Refractive Index, Opaque, Transparent, Speed of Light, Relative Refractive Index, Refraction and Snell’s Law, Refraction in Denser and Rarer Medium 42 min
        • Lecture14.2
          Image Formation due to Refraction; Derivation; Refraction and Image formation in Glass Slab 57 min
        • Lecture14.3
          Total Internal Reflection, Critical Angle, Principle of Reversibility 01 hour
        • Lecture14.4
          Application of Total Internal Reflection 45 min
        • Lecture14.5
          Refraction at Curved Surface, Image Formation by Curved Surface, Derivation 56 min
        • Lecture14.6
          Image Formation by Curved Surface, Snell’s Law in Vector Form 01 hour
        • Lecture14.7
          Lens, Various types of Lens, Differentiating between various Lenses; Optical Centre, Derivation of Lens Maker Formula 01 hour
        • Lecture14.8
          Lens Formula, Questions and Answers 39 min
        • Lecture14.9
          Property of Image by Convex and Concave Lens; Lens Location, Minimum Distance Between Real Image and Object 01 hour
        • Lecture14.10
          Power of Lens, Combination of Lens, Autocollimation 35 min
        • Lecture14.11
          Silvering of Lens 44 min
        • Lecture14.12
          Cutting of Lens and Mirror, Vertical Cutting, Horizontal Cutting 49 min
        • Lecture14.13
          Newton’s Law for Lens and Virtual Object 01 hour
      • 15.Ray Optics (Part 3)
        6
        • Lecture15.1
          Prism, Angle of Prism, Reversibility in Prism 51 min
        • Lecture15.2
          Deviation in Prism, Minimum and Maximum Deviation, Asymmetric, Thin Prism, Proof for formula of Thin Prism 59 min
        • Lecture15.3
          Dispersion of Light, Refractive Index, Composition of Light, Dispersion through Prism 01 hour
        • Lecture15.4
          Rainbow Formation, Scattering of Light, Tyndall Effect, Defects of Image, Spherical Defect, Chromatic Defect, Achromatism. 57 min
        • Lecture15.5
          Optical Instruments, The Human Eye, Defects of Eye and its Corrections 01 hour
        • Lecture15.6
          Microscope & Telescope 02 hour
      • 16.Wave Optics
        21
        • Lecture16.1
          Introduction to Wave Optics 11 min
        • Lecture16.2
          Huygens Wave Theory 14 min
        • Lecture16.3
          Huygens Theory of Secondary Wavelets 10 min
        • Lecture16.4
          Law of Reflection by Huygens Theory 10 min
        • Lecture16.5
          Deriving Laws of Refraction by Huygens Wave Theory 10 min
        • Lecture16.6
          Multiple Answer type question on Huygens Theory 41 min
        • Lecture16.7
          Conditions of Constructive and Destructive Interference 22 min
        • Lecture16.8
          Conditions of Constructive and Destructive Interference 06 min
        • Lecture16.9
          Conditions of Constructive and Destructive Interference 23 min
        • Lecture16.10
          Incoherent Sources of Light 38 min
        • Lecture16.11
          Youngs Double Slit Experiment 12 min
        • Lecture16.12
          Fringe Width Positions of Bright and Dark Fringes 15 min
        • Lecture16.13
          Numerical problems on Youngs Double Slit Experiment 11 min
        • Lecture16.14
          Numerical problems on Youngs Double Slit Experiment 19 min
        • Lecture16.15
          Displacement of Interference Pattern 19 min
        • Lecture16.16
          Numerical problems on Displacement of Interference Pattern 28 min
        • Lecture16.17
          Shapes of Fringes 37 min
        • Lecture16.18
          Colour of Thin Films 59 min
        • Lecture16.19
          Interference with White Light 32 min
        • Lecture16.20
          Chapter Notes – Wave Optics
        • Lecture16.21
          NCERT Solutions – Wave Optics
      • 17.Atomic Structure
        6
        • Lecture17.1
          Thomson and Rutherford Model of Atom; Trajectory of Alpha particle; Bohr’s Model ; Hydrogen Like Atom; Energy Levels 58 min
        • Lecture17.2
          Emission Spectra, Absorption Spectra; De Broglie Explanation of Bohr’s 2nd Postulate; Limitations of Bohr’s Model 37 min
        • Lecture17.3
          Momentum Conservation in Photon Emission, Motion of Nucleus, Atomic Collision 58 min
        • Lecture17.4
          Chapter Notes – Atomic Structure
        • Lecture17.5
          NCERT Solutions – Atomic Structure
        • Lecture17.6
          Revision Notes Atomic Structure
      • 18.Nucleus
        6
        • Lecture18.1
          Basics- Size of Nucleus, Nuclear Force, Binding Energy, Mass Defect; Radioactive Decay 01 hour
        • Lecture18.2
          Laws of Radioactive Decay 36 min
        • Lecture18.3
          Nuclear Fission; Nuclear Reactor; Nuclear Fusion- Reaction Inside Sun 30 min
        • Lecture18.4
          Chapter Notes – Nucleus
        • Lecture18.5
          NCERT Solutions – Nucleus
        • Lecture18.6
          Revision Notes Nucleus
      • 19.X-Ray
        4
        • Lecture19.1
          Electromagnetic Spectrum, Thermionic Emission; Coolidge Tube – Process 1 22 min
        • Lecture19.2
          Coolidge Tube – Process 2; Moseley’s Law; Absorption of X-rays in Heavy Metal 39 min
        • Lecture19.3
          Chapter Notes – X-Ray
        • Lecture19.4
          Revision Notes X-Ray
      • 20.Error and Measurement
        2
        • Lecture20.1
          Least Count of Instruments; Mathematical Operation on Data with Random Error 18 min
        • Lecture20.2
          Significant Digits; Significant Digits and Mathematical Operations 30 min
      • 21.Semiconductors
        9
        • Lecture21.1
          Conductor, Semiconductors and Insulators Basics Difference, Energy Band Theory, Si element 21 min
        • Lecture21.2
          Doping and PN Junction 01 hour
        • Lecture21.3
          Diode and Diode as Rectifier 01 hour
        • Lecture21.4
          Voltage Regulator and Zener Diode and Optoelectronic Jn. Devices 01 hour
        • Lecture21.5
          Transistor, pnp, npn, Modes of operation, Input and Output Characteristics, , Current Amplification Factor 01 hour
        • Lecture21.6
          Transistor as Amplifier, Transistor as Switch, Transistor as Oscillator, Digital Gates 01 hour
        • Lecture21.7
          Chapter Notes – Semiconductors
        • Lecture21.8
          NCERT Solutions – Semiconductors
        • Lecture21.9
          Revision Notes Semiconductors
      • 22.Communication Systems
        5
        • Lecture22.1
          Basic working and terms; Antenna; Modulation and Types of Modulation 32 min
        • Lecture22.2
          Amplification Modulation, Transmitter, Receiver, Modulation index 40 min
        • Lecture22.3
          Chapter Notes – Communication Systems
        • Lecture22.4
          NCERT Solutions – Communication Systems
        • Lecture22.5
          Revision Notes Communication Systems

        Chapter Notes – Electrostatics (2)

        Charge is the property of matter that causes it to produce and experience electrical and magnetic effects. The study of the electrical charges at rest is called electrostatics. When both electrical and magnetic effects are present, the interaction between charges is referred to as electromagnetic.

        There exist two types of charges in nature : positive and negative. Like charges repel, and unlike charges attract, each other.

        The type of charge on an electron is negative. The charge of a proton is the same as that of an electron but with a positive sign. In an atom, the number of electrons and the number of protons are equal. The atom is, therefore, electrically neutral. If one or more electrons are added to it, it becomes negatively charged and is designated as negative ion. However, if one or more electrons are removed from an atom, it becomes positively charged and is called a positive ion.

        The excess or deficiency of electrons in a body gives the concept of charge. If there is an excess of electrons in a body, it is negatively charged. And if there is deficiency of electrons, the body becomes positively charged. Whenever addition or removal of electrons takes places, the body acquires a charge.

        The SI Unit of charge is coulomb (C). In SI units, the current is a fundamental quantity, having a unit of ampere (A). The unit of charge is defined in terms of the unit of current. Thus, one coulomb is the charge transferred in one second across the section of a wire carrying a current of one ampere.

        As    q = It, we have
        1 C = (1 A) (1 s)

        The dimensions of charge are [A T].

        Properties of Charge

        (1)  Quantization of Charge :  Electric charge can have only discrete values, rather than any value. That is, charge is quantized. The smallest discrete value of charge that can exist in nature is the charge on an electron, given as

        e =  ± 1.6 x 10– 19 C

        This is the charge attained by an electron and a proton.
        A charge q must be an integral multiple of this basic unit. That is,

        Q = ± ne          where n = 1, 2, …

        Charge on a body can never be (½)e, (2/3)e, or 5.7e, etc.
        When we rub a glass rod with silk, some electrons are transferred from the rod to the silk. The rod becomes positively charged. The silk becomes negatively charged. The coulomb is a very large amount of charge. A typical charge acquired by a rubbed body is 10 – 8 C.

        Application  1
        A body is having a charge of +0.32 C. How many electrons have been added to or removed from it ?

        Solution:

        Given q = +0.32 C. Since the charge is positive, there is deficiency of electrons.

        n=qe=0.321.6×10−19 = 2 x 1018 electrons

        Note that the electron itself is not the charge; charge is a property, like mass, of elementary particles, such as the electrons, protons, etc.

        (2) Charge is Always Associated with Mass : A charge cannot exist without mass, though a mass can exist without charge. The particles such as photon or neutrino have no (rest) mass. Hence, these particles can never have a charge.
        The mass of a body (slightly) increases when it acquires a negative charge (by gaining some electrons). On the other hand, when a body acquires a positive charge (by losing some electrons), its mass (slightly) decreases.

        (3) Conservation of Charge : In an isolated system, the total charge remains constant. In other words, charge can neither be created nor destroyed. It can be transferred from one body to the other. Or, equal amounts of positive or negative charges can appear or disappear. This is what happens in pair production and pair annihilation, as shown in figure.

        Note that in pair production and pair annihilation, neither mass nor energy is conserved separately, but (mass + energy) is conserved. In pair production energy is converted into mass, while in annihilation mass is converted into energy.
        Conservation of charge holds good in all types of reactions.
        For example :
        Chemical Reaction :

        Na+    +     Cl–  →   NaCl
        Charge :   (+e)   +   (-e)   =  (0)

        Radioactive Decay :

        n         →     p          +          e–             +           v¯

                                            Neutron                proton              electron         antineutrino

        Charge :          (0)        =       (+e)      +       (-e)          +         (0)

        (4) Invariance of Charge :  Numerical value of a charge is independent of the frame of reference. It means the value of charge on a body remains the same, whether it is stationary, or moving with a constant velocity or accelerating. In contrast, the mass of a body depends on its speed, and it decreases with increase in speed.

        COULOMB’S LAW

        The force of interaction of two stationary point charges in vacuum is directly proportional to the product of these charges and inversely proportional to the square of their separation,

        F=kq1q2r2

        where F is in newton, q1 and q2 in coulomb, r in metre, and k is a constant given in SI units by

        k=14π∈0 = 9 x 109 N m2 C–2

        where ∈0 = 8.85 ´ 10–12 C2 N–1 m–2 and is called the permittivity of free space (vacuum or air).
        For mediums other than air or vacuum, the electrostatic force between two charges becomes

        F=14π∈.q1q2r2=14πε0∈r.q1q2r2

        Here ∈=∈0∈r, is called the absolute permittivity or permittivity of the medium, and ∈r=∈∈0 is the relative permittivity of the medium which is a dimensionless constant. ∈r is also sometimes called dielectric constant, and is represented by letter K.

        The coulomb force acts along the straight line connecting the points of location of the charges.
        This force is central and spherically symmetric.
        The vector form of Coulomb’s law is F⃗ =kq1q2r2r^. The unit vector  has its origin at the source of the force.
        For example, to find the force on q2, the origin of r is placed at q1 as shown in the figure. If F is the magnitude of the force (a positive scalar), then
        F⃗ =+Fr^          means a repulsion
        whereas,  F⃗ =−Fr^            means an attraction

        Analogy with Gravitation Law

        Coulomb’s law is analogous to Newton’s law of gravitation :

        F=Gm1m2r2

        However, following are the important differences :
        (a)  Electric force between charged particles is much stronger than gravitational force, i.e., FE >> FG. This is why when both FE and FG are present, we neglect FG
        (e.g. between two electrons FG = 10–39 FE).
        (b)  Electric force can be attractive or repulsive. But the gravitational force is always attractive.
        (c)  Electric force depends on the nature of medium between the charges, but gravitational force does not.

        Important Points Regarding Coulomb’s Law

        (1)  Charges are Assumed to be at Rest :  When charges are in motion they also produce and experience magnetic forces.

        (2) Charges are Assumed to be on Point Particles : Coulomb’s law cannot be directly applied to a finite charge distribution. In such a case (see figure), it is not possible to definitely specify the separation between the charges. However, there is an exception. When the charge is distributed uniformly over a spherical surface, the force on a point charge outside the surface may be computed from Coulomb’s law by treating the charge on the sphere as if it were concentrated at the centre.

        Principle of Superposition

        The coulomb’s law obeys the principle of superposition. It means that the force between two particles is not affected by the presence of other charges. This principle is used to find the net force exerted on a given charged particle by other charged particles.
        The force on a charged particle q1 due to point charges q2, q3 and q4 is the resultant of forces due to individual point charges, i.e.,
        F⃗ 1=F⃗ 12+F⃗ 13+F⃗ 14
        Note that the notation represents the force on q1 due to q­2.

        How to Solve a Problem using Coulomb’s Law ?

        (1)  Decide whether the force due to a given charge is attractive or repulsive and show it by drawing vector, pointing towards or away from the given charge, respectively.
        (2)  Find the magnitude of the force using Coulomb’s law—ignoring the signs of the charges.
        (3)  Resolve the forces along the given co-ordinate axes and express them in vector form using i^,j^,k^ unit vector notation, unless otherwise specified.
        (4)  Use the principle of superposition to find the net force on the charge.

        Application 2
        Four point charges are located at the corners of a rectangle, as shown in figure. Find the net force acting on the charge q1
        Solution:(1)  The force F⃗ 12 (between q1 and q2) is repulsive, while the forces F⃗ 13 (between q1 and q3) and F⃗ 14 (between q1 and q4) are attractive.

        (2) The magnitude of the forces F⃗ 12, F⃗ 13 and F⃗ 14 are

        F12=kq1q2r212=(9×109)(8×10−9)(4×10−9)(3×10−2)2=32×10−5N
        F13=kq1q3r213=(9×109)(8×10−9)(8×10−9)(5×10−2)2=23×10−5N
        F14=kq1q4r214=(9×109)(8×10−9)(12×10−9)(4×10−2)2=54×10−5N

        (3)  F⃗ 12 =(−32×10−5)j^

        F⃗ 13 =(F13cosθ) i^ + +(F13sinθ) j^
        =[−(23)(45)i^+(23)(35)j^]×10−5
        =[−18.4i^+13.8j^]×10−5
        F⃗ 14 =(−54×10−5) i^

        (4)  The net force on q1 is

        F⃗ 1=F⃗ 12+F⃗ 13+F⃗ 14
        =[−72.4i^−18.2j^]×10−5N
        =[−72.4−18.2]×10−5N

        Application 3
        Five point charges, each +q are placed on five vertices of a regular hexagon of side L. What is the magnitude of the force on a point charge –q placed at the centre of the hexagon ?

        Solution:

        Had there been sixth charge +q at the remaining vertex of hexagon, the net force due to all the six charges on –q at O would be zero. The forces due to individual charges  will balance each other. That is,
        F→R=0
        Now if f⃗  is the force due to sixth charge and due to remaining five charges, we must have
        F⃗ R=F⃗ +f⃗ =0  i.e.,          F⃗ =−f⃗ 
        or      F=14πε0q×qL2=14πε0[qL]2

        Prev Connecting Two Conductors; Grounding of conductor; Electric field just outside conductor; Electrostatic pressure; Self potential Energy
        Next Current, Motion of Electrons in Conductor; Temp. Dependence of Resistor

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