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Lesson_4.2_Printable_PPT

Lesson_4.2_Printable_PPT - Magnetic Field of a Moving...

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Magnetic Field of a Moving Charge A moving point charge is equivalent to an electric current. The magnetic filed B at a point distance r from a charge q moving with a velocity v is directly proportional to the product q v and inversely proportional to the square of the distance r . r is a vector that points from q to the point where B is determined. 2 4 o qv B r μ π = q μ o is called the permeability of free space. μ o has an exact value given by μ o = 4 π × 10 -7 TmA -1 = 4 π × 10 -7 NA -2 If θ is the angle between v and the vector r , the magnitude of B can be written as 7 2 sin 10 qv B r θ - = http://www.youtube.com/watch?v=eWaA9RiLsno http://www.youtube.com/watch?v=eWaA9RiLsno r

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Example 1 A point charge of magnitude 4.5 nC is moving with a speed of v = 3.6 × 10 7 m.s -1 along the line y = 3. Find the magnetic filed at the origin produced by this charge when it is at the point (-4 m, 3 m). At the point (-4m, 3m), the distance r is 2 2 3 4 5 m r = + = V = 3.6 × 10 7 ms -1 i r θ 3 sin 0.6 θ = = = 3.89 × 10 -10 T 5 7 2 sin 10 qv B r θ - = 9 7 7 2 4.5 10 3.6 10 0.6 10 5 - × × × × = This field is perpendicular to both x and y axes and is directed along the negative z direction. B = - 3.89 × 10 -10 T k
Magnetic filed due to current in a straight wire. Since current is caused by the motion of electric charges, it is obvious that a wire carrying a current will have a magnetic field around it. Consider a small length d of a conductor carrying a current I . d θ P is a point distance r from d and the vector r makes an angle θ with P r I the direction of the current. The magnetic field dB at P due to the current I in the small segment of the conductor d is given by 2 sin 4 o Id dB r μ θ π = The direction of this magnetic field is right angles to both the vector r and d .

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This equation is known as the Biot-Savart law and can be used to obtain an expression for the magnetic field B at a point distance r form a long straight wire. 2 sin 4 o Id dB r μ θ π = http://www.youtube.com/watch?v=E-3yQqgu8OA&feature=related http://www.youtube.com/watch?v=FjNnRyLexNM&feature=related The field lines around the wire are concentric circles and the direction of the filed is given by the right band rule. 2 o I B r μ π =
Example 2 A vertical wire on the side of a building carries a direct current of 12.5 A. What is the magnitude of the magnetic field inside the building at a distance of 20 cm from the wire? 2 o I B r μ π = 7 4 10 12.5 A π π - × = 2 0.2 m 5 1.25 10 T - × =

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Force between two parallel wires Consider two parallel wires separated by a distance r , each carrying a current I in the same direction. The current in the top wire produces a magnetic field where the bottom wire is situated and the current in the bottom wire will produce a magnetic field where the top wire is situated.
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