Question

A long wire carrying a 10 A current perpendicular to the xy plane intersects the x-axis at x= 4.0 cm. A

second, parallel wire carrying 5.0 A current intersects the x-axis at 10 cm. At what point or points on the

x-axis is the magnetic field zero if the two currents are in the opposite directions? [similar to HW 24-10]

Your solution must include a neat diagram.

Answer 1

Answer 2

SOLUTION :

  

  

                                     X-Y PLANE

                     10A                                    5A                   Net B = 0

    |_________o____________________o___________.____

  0     4 cm      *              6 cm                  +      s cm         P

   |<————————————————>|

                               10 cm

                              X-axis

Let magnetic field at point P , s meters away from the wire carrying 5 A  be zer0.

Magnetic field B1 at point P due to wire carrying 10 A into the x y plane 

= µ0 * I1 / (2 • pi * ((10 - 4) + s) 

= µ0 * 10 / (2 pi (6 + s)) Tesla

Magnetic field B2 at point P due to wire carrying 5 A out of the x y plane 

=  - µ0 * I2 / (2 • pi * s) 

= - µ0 * 5 / (2 pi  s) Twsla

So net magnetic field at P  (zero) := B1 + B2 

=> B1 + B2 = 0 

=>  µ0 * 10 / (2 pi (6 + s))  -  µ0 * 5 / (2 pi  s)  = 0

=> 10/(6 + s) - 5/s = 0

=> 10s - 5(6 + s) = 0

=> 5s - 30 =m 0

=> 5s = 30

=> s = 30/5 = 6cm.

So point P is at x = 10 + s = 10 + 6 = 16 cm where net magnetic field is zero. (ANSWER)