A horizontal wire 0.1 m long carries a current of 5 A. Find the magntiude and diretion of the magnetic field, which can support the weight of the wire. Assume wire to be of mass `3xx10^-3 kg m^-1`

Explanation

Length of current carrying wire = `l = 0.1 m `
`I = 5A`
Magnetic field = B = ?
Mass of the wire = `m = 3 xx 10^3 kg m^(-1)`
Mass of 0.1 m long wire = mi. = ml
`= 3 xx 10^(-3) xx 0.1`
`= 3 xx 10^(-4) kg`
Magnetic field can support the weight of wire if weight of wire is balanced by the magnetic force (in upward direction) due to the magnetic field.
Weight of wire = Magnetic force acting on current carrying wire
`m.g = B I l`
`(ml)/(l) g/I = B`
`implies B = 3 xx 10^3 xx (9.8)/5`
`implies B = 5.88 xx 10^(3) T`.