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Suppose we have two thin, very long, perpendicular wires soldered to each other so they form a cross. What would electric field lines look like in the plane that wires form, and would it be possible to calculate electric field at a point at distance $d$ from the wire crossing and on one of the $90°$ angle bisectors? Would it be easier to calculate electric field on the axis perpendicular to the wires plane and going trough wire crossing?

This question is purely a product of imagination and not a real task. I am not even aware of the complexity of the problem but would like to know if it's possible to do such calculations.

UPDATE: Both wires are, of course, carrying charge of linear charge density $\alpha$.

Suppose we have two thin, very long, perpendicular wires soldered to each other so they form a cross. What would electric field lines look like in the plane that wires form, and would it be possible to calculate electric field at a point at distance $d$ from the wire crossing and on one of the $90°$ angle bisectors? Would it be easier to calculate electric field on the axis perpendicular to the wires plane and going trough wire crossing?

This question is purely a product of imagination and not a real task. I am not even aware of the complexity of the problem but would like to know if it's possible to do such calculations.

Suppose we have two thin, very long, perpendicular wires soldered to each other so they form a cross. What would electric field lines look like in the plane that wires form, and would it be possible to calculate electric field at a point at distance $d$ from the wire crossing and on one of the $90°$ angle bisectors? Would it be easier to calculate electric field on the axis perpendicular to the wires plane and going trough wire crossing?

This question is purely a product of imagination and not a real task. I am not even aware of the complexity of the problem but would like to know if it's possible to do such calculations.

UPDATE: Both wires are, of course, carrying charge of linear charge density $\alpha$.

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user16688
user16688

Electric field of a cross-like conductor

Suppose we have two thin, very long, perpendicular wires soldered to each other so they form a cross. What would electric field lines look like in the plane that wires form, and would it be possible to calculate electric field at a point at distance $d$ from the wire crossing and on one of the $90°$ angle bisectors? Would it be easier to calculate electric field on the axis perpendicular to the wires plane and going trough wire crossing?

This question is purely a product of imagination and not a real task. I am not even aware of the complexity of the problem but would like to know if it's possible to do such calculations.