Three long wires are parallel to a z axis, and each

Problem 69

Three long wires are parallel to a z axis, and each carries a current of 10 A in the positive z direction.Their points of intersection with the xy plane form an equilateral triangle with sides of 50 cm, as shown in the figure. A fourth wire (wire b) passes through the midpoint of the base of the triangle and is parallel to the other three wires. If the net magnetic force on wire a is zero, what are the (a) size and (b) direction (&z or %z) of the current in wire b?

                                                           Step by Step Solution

Step 1 of 2

a.

Take wire at the bottom as wire , wire at the bottom right as wire

Given  and

By Fleming’s the right hand rule, the magnetic field   (evaluated at point ‘a’) produced    by wire 1 is at (measured counterclockwise from the axis,in the  plane),and the field produced by wire 2 is . By symmetry   we observe that only the  components survive,resulting

Now use the equation  …….(a). To cancel this,wire  must carry current into the page( direction) of value.

 and equation can be used