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Unformatted text preview: Lesson 4.2 Magnetic Field Calculations 1. Magnetic field of a moving point charge A moving point charge is equivalent to an electric current. Therefore it is reasonable to assume that there will be a magnetic filed associated with a moving charge. 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. Since B is a vector, w can write this as where is a unit vector that points from q to the point where B is determined. The constant of proportionality in this case is where o is called the permeability of free space. It should be noted here that o is not the same as , the magnetic moment we discussed in the last lesson. o has an exact value given by o = 4 107 TmA1 = 4 107 NA2 If is the angle between v and the unit vector, the magnitude of B can be written as 7 2 sin 10 qv B r  = Example 1 A point charge of magnitude 4.5 nC is moving with a speed of v = 3.6 107 ms 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). Solution At the point (4m, 3m), the distance r is = 5 m r 3.6 10 7 ms1 i = 3.89 1010 T This field is perpendicular to both x and y axes and is directed along the negative z direction. B = 3.89 1010 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. P is a point distance r from dl and the vector r makes an angle with the direction of the current. The magnetic field dB at P due to the current I in the small segment of the conductor dl is given by 2 sin 4 o Id dB r = The direction of this electric field is right angles to both the vector r and d . This equation is known as the BiotSavart law and can be used to obtain an expression for the magnetic field B at a point distance r form a long straight wire. B is given by 2 o I B r = The field lines around the wire are concentric circles and the direction of the filed is given by the right band rule. r P d I If you wrap the four fingers of your right hand around the conductor carrying a current I such that the thumb indicates the direction of the current as shown in the figure on the right, then the direction of the magnetic field B caused by the current I will be the direction in which you wrap your four fingers on the conductor. Reversing the direction of I will reverse the direction of B. 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?...
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This note was uploaded on 05/01/2011 for the course PHY 2049 taught by Professor George during the Spring '11 term at Edison State College.
 Spring '11
 George
 Physics, Charge, Current

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