A long straight telephone cable contains six wires, each carrying a current of `0*5A`. The distance between wires can be neglected. What is the magnitude of the magnetic field at a distance `10cm` from the cable, (i) if the currents in all the six wires are in the same direction (b) if four wires carry currents in one direction and the other two in opposite direction?

Explanation

(a) Total current, `I=0*5xx6=3*0A`
`B=(mu_0)/(4pi)(2I)/(r)=10^-7xx(2xx3*0)/(0*10)=6*0xx10^-6T`
(b) Effective current,
`I^'=0*5xx4-0*5xx2=1*0A`
`B^'=(mu_0)/(4pi)(2I^')/(r)=10^-7xx(2xx1*0)/(0*10)=2xx10^-6T`