Two point dipoles $p \hat{k}$ and $\frac{p}{2} \hat{k}$ are located at (0,0,0) and (1m,0,2m). Find the field at the point (1,0,0).

Question

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Answer 1

The given point is on axis of $\frac{p ˉ}{2}$ dipole and at equatorial line of $\overset{p}{ˉ}$ dipole so that field at given point is $(\overset{ˉ}{E_{1}} + \overset{ˉ}{E_{2}})$
$\overset{ˉ}{E_{1}} = \frac{2 K ( p / 2 )}{2 ^{3}} = \frac{K p}{8} (+ \hat{k})$
$\overset{ˉ}{E_{2}} = \frac{K p}{1} (- \hat{k})$
$\overset{ˉ}{E_{1}} + \overset{ˉ}{E_{2}} = \frac{7}{8} K p (- \hat{k}) = - \frac{7 p}{3 2 π ε _{0}} \hat{k}$

Answer 2

The given point is on axis of

\frac{p ˉ}{2}

dipole and at equatorial line of

\overset{p}{ˉ}

dipole so that field at given point is

(\overset{ˉ}{E_{1}} + \overset{ˉ}{E_{2}})

\overset{ˉ}{E_{1}} = \frac{2 K ( p / 2 )}{2 ^{3}} = \frac{K p}{8} (+ \hat{k})

\overset{ˉ}{E_{2}} = \frac{K p}{1} (- \hat{k})

\overset{ˉ}{E_{1}} + \overset{ˉ}{E_{2}} = \frac{7}{8} K p (- \hat{k}) = - \frac{7 p}{3 2 π ε _{0}} \hat{k}