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5 - MAGNETIC EFFECTS OF ELECTRIC CURRENT AND MAGNETISM Page 1 Introduction The branches of electricity and magnetism were unified by scientists like Oersted, Rowland, Faraday, Maxwell and Lorentz. The branch of physics covering a combined study of electricity and magnetism is known as electromagnetism or electrodynamics. It is useful in study of subjects like plasma physics, magneto-hydrodynamics and communication. 5.1 Oersted’s Observation In 1819 A.D., Oersted, a school teacher from Denmark, observed that magnetic field is produced around a wire carrying electric current. If a conducting wire is kept parallel to the magnetic needle and electric current is passed through it, needle gets deflected and aligns itself perpendicularly to the length of the wire. 5.2 Biot-Savart’s Law The intensity of magnetic field due to a current element Ι dl at a point having position vector r with respect to the electric current element is given by the formula 2 0 0 0 r θ sin dl 4 μ = dB and 3 r r × dl 4 μ = 2 r ^ r × dl 4 μ = dB ΙΙ ΙΙ π ΙΙ π π l l , where dB = magnetic intensity in tesla ( T ) or weber / // m 2 , ΙΙ dl = current element ( product of electric current and length of small line element dl of the conductor ) 0 μ = magnetic permeability of vacuum = 4 π ππ × 10 - 7 tesla metre per ampere ( T m A - 1 ) ^ r = unit vector along the direction of r = l l r r and θ = angle between dl and r The direction of dB is perpendicular to the plane formed by dl and r . As dl and r are taken in the plane of the figure, the direction of dB is perpendicular to the plane of the figure and going inside it, as shown by . On integrating the above equation, we get the total intensity at the point P due to the entire length of the conducting wire as π Ι = 4 B 0 μ × 2 r ^ r dl or π Ι = 4 B 0 μ × 3 r r dl
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5 - MAGNETIC EFFECTS OF ELECTRIC CURRENT AND MAGNETISM Page 2 5.3 Some Applications of Biot-Savart’s Law 5.3 ( a ) Magnetic field due to a straight conductor carrying electric current A straight conductor AB carrying electric current Ι is kept along X-axis as shown in the figure. It is desired to find magnetic intensity at a point P located at a perpendicular distance y from the wire. Y-axis is along OP. A small current element Ι ΙΙ dx ^ i is at a distance x from the origin on the wire. By Biot-Savart’s law, magnetic intensity at point P due to this current element is 3 0 r r dx 4 dB μ × ΙΙ π = ( 1 ) Putting dx = ^ i dx and r = ^ i x ^ j y - ( from OPQ formed by vectors ) × r dx = i dx ^ × ^ i x ^ j y - = y dx ^ k dB = 3 ^ 0 r k dx y 4 μ ΙΙ π This field is perpendicular to the plane formed by dx and r coming out normally from the plane of the figure. Integrating over the whole length of the wire, B = dB
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This note was uploaded on 11/28/2011 for the course PHYSICS 300 taught by Professor Smith during the Spring '06 term at ITT Tech Flint.

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