Calculating electric dipole moment

Electricity and Magnetism Level 2

A 2 C 2 \text{ C} charge is placed at ( 0 m , 3 m ) (0\text{ m},3\text{ m}) and a − 2 C -2\text{ C} charge is at ( 4 m , 0 m ) . (4\text{ m},0\text{ m}). What is the electric dipole moment?

− 8 x ^ + 6 y ^ -8 \hat{x} + 6 \hat{y} 8 x ^ − 6 y ^ 8 \hat{x} - 6 \hat{y} 4 x ^ − 3 y ^ 4 \hat{x} - 3 \hat{y} − 4 x ^ + 3 y ^ -4 \hat{x} + 3 \hat{y}

July Thomas by July Thomas , 30, USA

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1 solution

July Thomas
Jun 9, 2016

The electric dipole moment is p ⃗ = q d ⃗ \vec{p} = q\vec{d} where d ⃗ \vec{d} points from the negative charge to the positive charge. Hence,

d ⃗ = ( 0 − 4 ) x ^ + ( 3 − 0 ) y ^ = − 4 x ^ + 3 y ^ . \vec{d} = (0-4)\hat{x} + (3-0)\hat{y} = -4\hat{x} + 3\hat{y}.

p ⃗ = q d ⃗ = ( 2 ) ( − 4 x ^ + 3 y ^ ) = − 8 x ^ + 6 y ^ \vec{p} = q\vec{d} = (2) (-4\hat{x} + 3\hat{y}) = -8\hat{x} + 6\hat{y}

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