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Magnetostatics, , Magnetic Field:Study of magnetic field produced due to steady current is called as magnetostatics., Magnetic field is a space around a magnetic material or a moving electric charge within which the, force of magnetism acts. Earth bar magnet,current carrying straight conductor, loop of wire and, solenoid are the source of magnetic field., Magnetic field is schematically represented by magnetic lines of force is called as lines of, magnetic induction. The lines of induction collectively called as flux. The magnitude of magnetic field, is measured in Tesla(T) or Weber per metre2 in SI unit and gauss in CGS units., 1 tesla = 1 Wb/m2 = 1 N/Am = 104 gauss, Magnetic field is a vector field because at any point it has both direction and magnitude., Magnetic Flux(Ф):Magnetic field is represented by magnetic lines of force called as line of magnetic induction., The concentration of lines of induction represents the field strength.The magnetic flux is proportional, to number of lines of induction passing through a unit area of cross section.The magnetic flux through, a surface is surface integral of normal component of magnetic field B passing through that surface., ⃗ ⃗, Φ= B., Acosθ, Where B is the magnitude of magnetic field, A is a area of surface and Ф is the angle between, magnetic field lines and normal to the surface., Magnetic intensity at a point is related to magnetic field for magnetic induction at that point by, ⃗ H, ⃗ , where μ0 is a constant called permeability of free space, Bμ, 0, SI unit of magnetic flux is Weber and CGS maxwell. magnetic flux is measured with flux, metre., Lorentz force :Consider moving charge q in magnetic field experience a force called as magnetic force. If the, charge q is moving charge and v is its velocity and θ is angle between direction of velocity and, magnetic induction. The magnetic force is given by, ⃗ ….... Lorentz force law, ⃗ × B), F⃗m q( v, In magnitude F m qvBsinθ, ⃗ i.e. given by, This force is directed at right angle to the plane containing vector ⃗, v and B, right hand rule, If a point charge q is moving in a region where there is electric field E as well as magnetic field B, the, total force experienced is called as Lorentz force and is given by, ⃗, ⃗ q( v, ⃗, ⃗ × B), F=q, E+, ⃗, F=q, E+q v B sinθ, ⃗, F=q( E+v Bsin θ), This equation is called as Lorentz force equation.

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Biot-savart law :consider a conductor AB through which current is flowing in the direction as shown in figure, 7.6, Let p be any point at a distance r from the centre of current element where length element, ⃗, i dl is infinitesimally small and considered as a straight line element., Let ⃗, r be the position of p with respect to current element. Let θ be the angle, ⃗ .The direction of dl, ⃗ is the direction of current., between ⃗, r and dl, According to Biot-savart law,Magnetic field at point p due to current element is, 1) directly proportional to the strength of the current element, 2) directly proportional to sin of angle between element and, 3) are are inversely proportional to square of distance, ⃗, ⃗ and ⃗, 4) dB is perpendicular to the plane formed by dl, r and its direction is given, by right hand rule, I dlsin θ, r2, I dlsin θ, dB=K, r2, In CGS system units,K= 1 and in MKS system of unit K = µ0 /4Π, where µ0 is called permeability of free space., μ I dl sinθ, dB= 0, 4π, r2, In vector form, , dB ∝, , ⃗ ⃗, μ 0 I dl×, r, ⃗, dB=, 3, 4π r, For finite length of steady current the law can be written as, ⃗ r, ⃗ μ 0 I ∫ dl×⃗, dB=, ….........I, 4 π length r 3, ⃗ due to entire length of current carrying conductor, equation (I) give the magnetic induction B