Magnetic field of a circular loop off axis


  • Telangana TSBIE Intermediate Syllabus Reduced by 30 Percent due to covid-19 pandemic
  • Magnetic Field on the Axis of a Circular Current Loop: Elaboration, Formula, Sample Problem
  • Magnetic field due to a current through circular loop
  • At the centre of a current carrying single turn circular loop, the magnetic field is
  • Telangana TSBIE Intermediate Syllabus Reduced by 30 Percent due to covid-19 pandemic

    Electromagnetic waves and their characteristics qualitative ideas only. Transverse nature of electromagnetic waves. Electromagnetic spectrum radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays including elementary facts about their uses. Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism.

    Scattering of light- blue colour of the sky and reddish appearance of the sun at sunrise and sunset. Optical instruments: Human eye, image formation and accommodation, correction of eye defects myopia and hypermetropia using lenses. Microscopes and astronomical telescopes reflecting and refracting and their magnifying powers.

    Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Matter waves- wave nature of particles, de Broglie relation. Davisson-Germer experiment experimental details should be omitted; only conclusion should be explained.

    Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Massenergy relation, mass defect; binding energy per nucleon and its variation with mass number, nuclear fission and fusion. UNIT IX: Electronic Devices Energy bands in solids qualitative ideas only , conductors, insulators and semiconductors; semiconductor diode- I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator.

    Junction transistor, transistor action, characteristics of a transistor; transistor as an amplifier common emitter configuration and oscillator. Transistor as a switch. Atomic and molecular masses. Mole concept and molar mass; percentage composition and empirical and molecular formula; chemical reactions, stoichiometry and calculations based on stoichiometry.

    UNIT III: Classification of Elements and Periodicity in Properties Modern periodic law and long form of periodic table, periodic trends in properties of elementsatomic radii, ionic radii, ionization enthalpy, electron gain enthalpy, electronegativity, valence.

    UNIT IV: Chemical Bonding and Molecular Structure Valence electrons, ionic bond, covalent bond, bond parameters, Lewis structure, polar character of covalent bond, valence bond theory, resonance, geometry of molecules, VSEPR theory, concept of hybridization involving s, p and d orbitals and shapes of some simple molecules, molecular orbital theory of homonuclear diatomic molecules qualitative idea only.

    Hydrogen bond. Avogadro number, ideal gas equation. Kinetic energy and molecular speeds elementary idea , deviation from ideal behaviour, liquefaction of gases, critical temperature.

    Liquid State- Vapour pressure, viscosity and surface tension qualitative idea only, no mathematical derivations.

    Introduction of entropy as state function, Second law of thermodynamics, Gibbs energy change for spontaneous and non-spontaneous process, criteria for equilibrium and spontaneity.

    Third law of thermodynamics- Brief introduction. Concept of oxidation and oxidation and reduction, redox reactions oxidation number, balancing redox reactions in terms of loss and gain of electron and change in oxidation numbers. UNIT IX: Hydrogen Occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides-ionic, covalent and interstitial; physical and chemical properties of water, heavy water; hydrogen peroxidepreparation, reactions, uses and structure; UNIT X: s-Block Elements Alkali and Alkaline earth metals Group I and group 2 elements: General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties such as ionization enthalpy, atomic and ionic radii , trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses.

    Preparation and Properties of Some important Compounds: Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogencarbonate, biological importance of sodium and potassium. Industrial use of lime and limestone, biological importance of Mg and Ca. Group 13 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; Boron, some important compounds: borax, boric acids, boron hydrides.

    Aluminium: uses, reactions with acids and alkalies. General 14 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous behaviour of first element. Carbon, allotropic forms, physical and chemical properties: uses of some important compounds: oxides. Important compounds of silicon and a few uses: silicon tetrachloride, silicones, silicates and zeolites, their uses.

    Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyper conjugation. Homolytic and heterolytic fission of a covalent bond: free radials, carbocations, carbanions; electrophiles and nucleophiles, types of organic reactions. UNIT XIII: Hydrocarbons Alkanes- Nomenclature, isomerism, conformations ethane only , physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis.

    Alkynes-Nomenclature, structure of triple bond ethyne , physical properties, methods of preparation, chemical reactions: acidic character of alkynes, addition reaction of- hydrogen, halogens, hydrogen halides and water.

    UNIT XIV: Environmental Chemistry Environmental pollution: Air, water and soil pollution, chemical reactions in atmosphere, smogs, major atmospheric pollutants; acid rain ozone and its reactions, effects of depletion of ozone layer, greenhouse effect and global warmingpollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution. Van Hoff factor. UNIT IV: Chemical Kinetics Rate of a reaction average and instantaneous , factors affecting rates of reaction; concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant, integrated rate equations and half life only for zero and first order reactions ; concept of collision theory elementary idea, no mathematical treatment.

    Activation energy, Arrhenious equation. Adsorption-physisorption and chemisorption; factors affecting adsorption of gases on solids, catalysis homogeneous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: distinction between true solutions, colloids and suspensions; lyophillic, lyophobic multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsions- types of emulsions.

    UNIT VI: General Principles and Processes of Isolation of Elements Principles and methods of extraction- concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron.

    UNIT VII: p- Block Elements Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; preparation and properties of ammonia and nitric acid, oxides of nitrogen structure only ; Phosphorous- allotropic forms; compounds of phosphorous: preparation and properties of phosphine, halides PCI3, PCI5 and oxoacids elementary idea only. Group 16 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen: preparation, properties and uses; classification of oxides; ozone.

    Sulphur — allotropic forms; compounds of sulphur: preparation, preparation, properties and uses of sulphur dioxide; sulphuric acid: industrial process of manufacture, properties and uses, oxoacids of sulphur structures only.

    Group 17 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds oxoacids of halogens structures only. Group 18 elements: General introduction, electronic configuration, occurrence, trends in physical and chemical properties, uses.

    UNIT VIII: d and f Block Elements General introduction, electronic configuration, characteristics of transition metals, general trends in properties of the first row transition metals- metallic character, ionization enthalpy, oxidation states, ionic radii, colour, catalytic property, magnetic properties, interstitial compounds, alloy formation.

    Lanthanoids- electronic configuration, oxidation states, chemical reactivity, and lanthanoid contraction and its consequences. Actinoids: Electronic configuration, oxidation states and comparison with lanthanoids. Optical rotation. Haloarenes: Nature of C-X bond, substitution reactions directive influence of halogen for monosubstituted compounds only. Uses and environment effects of — dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT. UNIT XI: Alcohols, Phenols and Ethers Alcohols: Nomenclature, methods of preparation, physical and chemical properties of primary alcohols only ; identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses with special reference to methanol and ethanol.

    Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols. Ethers: Nomenclature, methods of preparation, physical and chemical properties uses. UNIT XII: Aldehydes, Ketones and Carboxylic Acids Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties; and mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses.

    Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses. Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary secondary and tertiary amines.

    Cyanides and Isocyanides- will be mentioned at relevant places. Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry. Proteins- Elementary idea of — amino acids, peptide bond, polypeptides, proteins, primary structure, secondary structure, tertiary structure and quaternary structure qualitative idea only , denaturation of proteins; enzymes.

    Hormones- Elementary idea excluding structure. Vitamins- Classification and function. Some important polymers: natural and synthetic like polyesters, bakelite; rubber, Biodegradable and non-biodegradable polymers. UNIT XVI: Chemistry in Everyday Life Chemicals in medicines- analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines. Chemicals in food- preservatives, artificial sweetening agents, elementary idea of antioxidants.

    Determine the magnetic field of an arc of current. The circular loop of Figure has a radius R, carries a current I, and lies in the xz-plane. What is the magnetic field due to the current at an arbitrary point P along the axis of the loop? Determining the magnetic field at point P along the axis of a current-carrying loop of wire. We can use the Biot-Savart law to find the magnetic field due to a current.

    We first consider arbitrary segments on opposite sides of the loop to qualitatively show by the vector results that the net magnetic field direction is along the central axis from the loop. From there, we can use the Biot-Savart law to derive the expression for magnetic field. Let P be a distance y from the center of the loop. From the right-hand rule, the magnetic field at P, produced by the current element is directed at an angle above the y-axis as shown.

    Since is parallel along the x-axis and is in the yz-plane, the two vectors are perpendicular, so we have where we have used Now consider the magnetic field due to the current element which is directly opposite on the loop.

    The magnitude of is also given by Figure , but it is directed at an angle below the y-axis. The components of and perpendicular to the y-axis therefore cancel, and in calculating the net magnetic field, only the components along the y-axis need to be considered. The components perpendicular to the axis of the loop sum to zero in pairs. Hence at point P: For all elements on the wire, y, R, and are constant and are related by Now from Figure , the magnetic field at P is where we have used As discussed in the previous chapter, the closed current loop is a magnetic dipole of moment For this example, so the magnetic field at P can also be written as By setting in Figure , we obtain the magnetic field at the center of the loop: This equation becomes for a flat coil of n loops per length.

    The magnetic field lines are shaped as shown in Figure. Notice that one field line follows the axis of the loop. This is the field line we just found. Also, very close to the wire, the field lines are almost circular, like the lines of a long straight wire. Sketch of the magnetic field lines of a circular current loop. Magnetic Field between Two Loops Two loops of wire carry the same current of 10 mA, but flow in opposite directions as seen in Figure. One loop is measured to have a radius of while the other loop has a radius of The distance from the first loop to the point where the magnetic field is measured is 0.

    What is the magnitude of the net magnetic field at point P? Two loops of different radii have the same current but flowing in opposite directions. The magnetic field at point P is measured to be zero. Strategy The magnetic field at point P has been determined in Figure. Since the currents are flowing in opposite directions, the net magnetic field is the difference between the two fields generated by the coils. Using the given quantities in the problem, the net magnetic field is then calculated.

    Solution Solving for the net magnetic field using Figure and the given quantities in the problem yields Significance Helmholtz coils typically have loops with equal radii with current flowing in the same direction to have a strong uniform field at the midpoint between the loops. A similar application of the magnetic field distribution created by Helmholtz coils is found in a magnetic bottle that can temporarily trap charged particles.

    See Magnetic Forces and Fields for a discussion on this. Check Your Understanding Using Figure , at what distance would you have to move the first coil to have zero measurable magnetic field at point P? RHR-2 gives the direction of the field about the loop. Conceptual Questions Is the magnetic field of a current loop uniform? What happens to the length of a suspended spring when a current passes through it? The spring reduces in length since each coil with have a north pole-produced magnetic field next to a south pole of the next coil.

    Two concentric circular wires with different diameters carry currents in the same direction. Describe the force on the inner wire. Problems When the current through a circular loop is 6. A flat, circular loop has 20 turns. The radius of the loop is Determine the magnitude of the magnetic field at the center of the loop. A circular loop of radius R carries a current I. At what distance along the axis of the loop is the magnetic field one-half its value at the center of the loop?

    Two flat, circular coils, each with a radius R and wound with N turns, are mounted along the same axis so that they are parallel a distance d apart. What is the magnetic field at the midpoint of the common axis if a current I flows in the same direction through each coil?

    For the coils in the preceding problem, what is the magnetic field at the center of either coil?

    Magnetic Field on the Axis of a Circular Current Loop: Elaboration, Formula, Sample Problem

    Question 2 How does the strength of the magnetic field at the centre of a circular coil of wire depends on the radius of coil? Question 3 How does the strength of the magnetic field at the centre of a circular coil of wire depends on the number of turns of wire in the coil? Question 4 How does the strength of the magnetic field at the centre of a circular coil of wire depends on strength of current flowing in the coil?

    Magnetic field due to a Current through Circular loop The magnetic field around a straight current carrying conductor or wire can be increased by bending the wire into circular loop. A circular loop is made up of large number of very small straight wires.

    Magnetic field due to a current through circular loop

    Making Connections: Relativity Hearing all we do about Einstein, we sometimes get the impression that he invented relativity out of nothing. Both the direction and the magnitude of the magnetic field produced by a current-carrying loop are complex. RHR-2 can be used to give the direction of the field near the loop, but mapping with compasses and the rules about field lines given in Magnetic Fields and Magnetic Field Lines are needed for more detail.

    There is a simple formula for the magnetic field strength at the center of a circular loop. This equation is very similar to that for a straight wire, but it is valid only at the center of a circular loop of wire. The similarity of the equations does indicate that similar field strength can be obtained at the center of a loop. Note that the larger the loop, the smaller the field at its center, because the current is farther away.

    Figure 2. The field is similar to that of a bar magnet. Magnetic Field Produced by a Current-Carrying Solenoid A solenoid is a long coil of wire with many turns or loops, as opposed to a flat loop. Because of its shape, the field inside a solenoid can be very uniform, and also very strong. The field just outside the coils is nearly zero. Figure 3 shows how the field looks and how its direction is given by RHR Figure 3. The field outside the coils is nearly zero. The magnetic field inside of a current-carrying solenoid is very uniform in direction and magnitude.

    Only near the ends does it begin to weaken and change direction. Note that B is the field strength anywhere in the uniform region of the interior and not just at the center.

    At the centre of a current carrying single turn circular loop, the magnetic field is

    Large uniform fields spread over a large volume are possible with solenoids, as Example 2 implies. Example 2. Calculating Field Strength inside a Solenoid What is the field inside a 2. This is the field line we just found. Also, very close to the wire, the field lines are almost circular, like the lines of a long straight wire. Sketch of the magnetic field lines of a circular current loop.

    Magnetic Field between Two Loops Two loops of wire carry the same current of 10 mA, but flow in opposite directions as seen in Figure.

    One loop is measured to have a radius of while the other loop has a radius of The distance from the first loop to the point where the magnetic field is measured is 0. What is the magnitude of the net magnetic field at point P? Two loops of different radii have the same current but flowing in opposite directions.

    The magnetic field at point P is measured to be zero. Strategy The magnetic field at point P has been determined in Figure. Since the currents are flowing in opposite directions, the net magnetic field is the difference between the two fields generated by the coils. Using the given quantities in the problem, the net magnetic field is then calculated.

    Solution Solving for the net magnetic field using Figure and the given quantities in the problem yields Significance Helmholtz coils typically have loops with equal radii with current flowing in the same direction to have a strong uniform field at the midpoint between the loops. A similar application of the magnetic field distribution created by Helmholtz coils is found in a magnetic bottle that can temporarily trap charged particles.

    See Magnetic Forces and Fields for a discussion on this. Check Your Understanding Using Figureat what distance would you have to move the first coil to have zero measurable magnetic field at point P?


    thoughts on “Magnetic field of a circular loop off axis

    1. Excuse for that I interfere � To me this situation is familiar. It is possible to discuss. Write here or in PM.

    Leave a Reply

    Your email address will not be published. Required fields are marked *