A wire of length 2 L is oriented along the x axis, with its midpoint at the orig

Question

A wire of length 2 L is oriented along the x axis, with its midpoint at the origin. The charge per unit length on the rod is ? ( x ) = ?_0 ( x/L ) , where ?_0 is a constant.

i) Find the electric field at the origin.

ii) Obtain an integral expression for the electric field due t o the rod at a point (0 ,y, 0) .

iii) Show that when y >> 0 , the electric field is the same as that due to a dipole at the orig in that is oriented along the x axis. What is the dipole moment of this equivalent dipole?

Please show all appropriate work, thank you.

Explanation / Answer

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