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A charge +q is carried from point A( r, ...

A charge +q is carried from point `A( r, 135^(@))` to point `B(r, 45^(@))` following a path, which is a quadrant of circle of radius r ( Fig. 3.97). If the dipole moment is P, find the work done by the external agent (assume short dipole).
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Text Solution

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`V = (k p cos theta)/(r^2)`
For `A, theta = 1.35^(@) , V_A = (k p cos 135^(@))/(r^2) = (- k p)/(sqrt(2 )r^2)`
For `B, theta = 45^(@), V_B = (k p cos 45^(@))/(r^2) = (K p)/(sqrt(2) r^2)`
`W = q(V_B - V_A) = (qsqrt(2) k p)/(r^2) = (1)/(4 pi epsilon_0) (sqrt(2) q p)/(r^2)`.
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