Irodov Problem 3.43

From Problem 3.9 Eqn 4, we already know that the field due to a ring of radius R with charge q at a distance x along its axis is given by,



Hence the electric field due to the two rings is given by,



For , we can use Taylor's series with l as the variable around zero and approximate the electric field as,








When the electric field becomes,



We also know that the potential due to a ring of radius R with charge q at a distance x along the axis is given by,





Hence, the potential due to the two rings is given by,





For , we can use Taylor's series with l as the variable around zero and approximate the potential as,

Irodov Problem 3.42

As shown in the figure the two infinitely long wires are perpendicular to the screen (coming out of the screen). For , the distances of the positive and negative wires from X are given by and respectively.

We know that the electric field due to a single long wire at a distance d acts radially outwards and is given by,



Hence the total electric field for two wires is given by,



The direction of the electric field being radially outwards.

The electric potential can now evalauted as,