Question

A long wire carrying a 6.0A current perpendicular to the xy-plane intersects the x-axis atx=?2.0cm. A second, parallel wire carrying a 3.0A current intersects the x-axis atx=+2.0cm.

a) At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?

b) At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A long wire carrying a 5.0 A current perpendicular to the xy-plane intersects the x-axis at x= - 2.0 cm . A second, parallel wire carrying a 3.5 A current intersects the x-axis at x=+ 2.0cm .

A). At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?

B). At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

answer

given

current in thefirst wire i = 5A

current in the second wire i = 3.5A

a) for x>2 cm and for x<2cm the magnetic fields due to the currents in the two wires add. the point where the two magnetic fields cancel lies on the x axis between the two wires .

let that point be x distance from the origin

from biot savat law magnetic field due to wire

B = ?_oi/ 2?r

then

?₀5A/2?( 0.020m+x) = ?₀3.5A/2?( 0.020m-x)

    5 ( 0.020m-x) = 3.5( 0.020m+x)

   x = 0.35cm

b) the magnetic fields due to the currents in teh wires add in the origion -2cm<x< 2cm

for x< -2cm the magnetic field subtract bu the field due to the current is always larger than the field due to 3A curent

however fo x> 2cm the two fields will cancel at a point on the x axis

let the point be a x away from the origion

?₀5A/2?(x+ 0.020m) = ?₀3.5A/2?(x- 0.020m)

x = 11.3cm