Two parallel horizontal conductors are suspended by two light vertical threads each 75 cm long. Each conductor has a mass of `40gm^-1`, and when there is no current they are 0.5 cm apart. Equal current in the two wires result in a separation of 1.5 cm. Find the values and directions of currents. Take `g=9.8ms^-2`.

Explanation

The situatation is shown in Fig.

Here, we have `T cos theta=mg…..(i)`
`Tsin theta=F=(mu_0)/(4pi) l (2i_1i_2)/d`
or `T sin theta=(mu_0)/(4pi) l (2i^2)/d….(ii)`
From Eqs. (i) and (ii) `tan theta=(mu_0)/(4pi) l (2i^2)/d.1/(mg)`
where `theta` is small, `tan theta~~ sin theta`
From the figure, `sin theta=(0.5xx10^-2)/(75xx10^-2) and m=40.0xx10^-3l kg`
where l=length of conductor in metre
Substituting in Eq. (iii), we get
`(0.5xx10^-2)/(75xx10^-2)=10^-7l (2i^2)/(1.5xx10^-2)xx1/((40xx10^-3)lxx9.8)`
Solving, we get `i=14A`
For repulsion, the currents are in opposite directions.