v4chap2 - Chapter 2 Electric Fields 2.1 2.1.1 The Important Stu The Electric Field Suppose we have a point charge q0 located at r and a set of external

v4chap2 - Chapter 2 Electric Fields 2.1 2.1.1 The Important...

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Chapter 2 Electric Fields 2.1 The Important Stuff 2.1.1 The Electric Field Suppose we have a point charge q 0 located at r and a set of external charges conspire so as to exert a force F on this charge. We can define the electric field at the point r by: E = F q 0 (2.1) The (vector) value of the E field depends only on the values and locations of the external charges, because from Coulomb’s law the force on any “test charge” q 0 is proportional to the value of the charge. However to make this definition really kosher we have to stipulate that the test charge q 0 is “small”; otherwise its presence will significantly influence the locations of the external charges. Turning Eq. 2.1 around, we can say that if the electric field at some point r has the value E then a small charge placed at r will experience a force F = q 0 E (2.2) The electric field is a vector . From Eq. 2.1 we can see that its SI units must be N C . It follows from Coulomb’s law that the electric field at point r due to a charge q located at the origin is given by E = k q r 2 ˆ r (2.3) where ˆ r is the unit vector which points in the same direction as r . 2.1.2 Electric Fields from Particular Charge Distributions Electric Dipole An electric dipole is a pair of charges of opposite sign ( ± q ) separated by a distance d which is usually meant to be small compared to the distance from the charges at which we 17
18 CHAPTER 2. ELECTRIC FIELDS MT69 MT113 MT114 MT40MT97MT41 MT69 MT113 MT114 MT40MT98MT41 Figure 2.1: The E

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