Question

14 cm length of wire carries a current of 1.5 A in the positive z direction. The force on this wire due to a magnetic field is = (-0.2 + 0.2 ) N. If this wire is rotated so that the current flows in the positive x direction, the force on the wire is = 0.2 N. Find the magnetic field

Answer 1

`0.95i+0.95j`

Step-by-step explanation:

We are given that

Length of wire,L=14 cm=
`(14)/(100)=0.14 m`

1 m=100 cm

Current,I=1.5 k A

Magnetic force,F=(-0.2i+0.2 J)N

Magnetic force,F=
`L(I* B)=0.14(1.5k*(B_xi+B_yj+B_zk))`

`-0.2i+0.2j=0.14(1.5B_xj-B_yi)=0.21B_xj-0.21B_yi`

By comparing on both sides

`0.2=0.21B_x`

`B_x=(0.2)/(0.21)0.95=0.95T`

`0.21B_y=0.2`

`B_y=(0.2)/(0.21)=0.95 T`

When the current flows in positive x direction

Then,
`F=0.2k N`

`0.2k=0.14(1.5i* (B_xi+B_yj+B_zk)`

`0.2k=0.21B_yk-0.21B_zj`

By comparing on both sides we get

`0.21B_z=0`

`B_z=0`

Magnetic field,
`B=B_xi+B_yj+B_zk=0.95i+0.95j`