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Vector Properties of the Magnetic Field

# Vector Properties of the Magnetic Field - Vector Properties...

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Vector Properties of the Magnetic Field Using vector calculus, we can generate some properties of any magnetic field, independent of the particular source of the field. Line Integrals of Magnetic Fields Recall that while studying electric fields we established that the surface integral through any closed surface in the field was equal to 4 Π times the total charge enclosed by the surface. We wish to develop a similar property for magnetic fields. For magnetic fields, however, we do not use a closed surface, but a closed loop. Consider a closed circular loop of radius r about a straight wire carrying a current I , as shown below. A closed path around a straight wire What is the line integral around this closed loop? We have chosen a path with constant radius, so the magnetic field at every point on the path is the same: B = . In addition, the total length of the path is simply the circumference of the circle: l = 2 Πr . Thus, because the field is constant on the path, the line integral is simply: lineintegral B

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