Answer to Question #126043 in Field Theory for Gabby

Question #126043
What is the strength of an electric field resulting from a dipole with a dipole moment of 25 C⋅m at a radius, r = 30 cm away and 75° from the y-axis?
1
Expert's answer
2020-07-13T11:43:04-0400

Let the direction of dipole is along the positive direction of x-axis.

Since,

"{\\displaystyle \\mathbf {E} \\left(\\mathbf {r} \\right)={\\frac {3\\left(\\mathbf {p} \\cdot {\\hat {\\mathbf {r} }}\\right){\\hat {\\mathbf {r} }}-\\mathbf {p} }{4\\pi \\varepsilon _{0}r^{3}}}\\ .}"

And,

"\\bold p=25\\hat{i}\\\\\n\\bold r=0.3(\\cos(15^\\circ)\\hat{i}+\\sin(15^\\circ)\\hat{j})"

Now.

"\\bold p\\cdot\\hat\\bold r=25\\cos(15^\\circ)"

Thus,

"\\bold E(\\bold r)=\\frac{9\\times 10^9}{0.3^3}(3(25\\cos(15^\\circ))(\\cos(15^\\circ)\\hat{i}+\\sin(15^\\circ)\\hat{j})-25\\hat{i}\\\\\n\\implies \\bold E=\\frac{10^{12}}{3}(44.97\\hat{i}+18.75\\hat j)\\\\\n\\implies E=16.24\\times10^{12}N\/C"


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