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E2chalsoln

# E2chalsoln - Phy sics 7B WS E2 Challenge Solution(rev 1.0...

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Physics 7B WS E2 Challenge Solution (rev. 1.0) Page 1 E-2 Challenge Problem - Solution Electric Field of a Dipole In this challenge problem we derive the form of the electric field very far from an electric dipole. Start with two charges, +q and -q, oriented along the z-direction in cylindrical coordinates and placed a distance d apart, centered on the origin. The dipole moment vector for this configuration of charges will be r p = qd ! z . We will find the electric field at a radial distance ρ from the axis and a distance z along the axis, in cylindrical coordinates. ( is used for the radial coordinate to distinguish it from the distance from the origin, r ) a) Call the vector pointing from the positive/negative charge to the point where we want to find the electric field r ± and the vector to the origin r . Write down what ! r ± (the unit vectors) and r (the magnitudes) are in terms of the cylindrical coordinates and the unit vectors ˆ r and ! z . We will first find r . This vector points from the origin to a point a radial distance from the z - axis and a height z up along the axis. Therefore, we can simply ‘follow’ the path that first takes us up a distance z to the point ( = 0, z ), and then radially out to the point ( , z ). We can make the two ‘legs’ of the path vectors and then add those vectors together to get the vector r .

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E2chalsoln - Phy sics 7B WS E2 Challenge Solution(rev 1.0...

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