Two parallel wires PQ, RS of resistance `10Omega` and `20Omega` are seperated by a distance of 10 cm and connected in parallel across a cell of emf200V and negligible intemal resistance. A wire AB of mass I g and length 1 cm is balanced exactly, between them. What must be the current in it.

Explanation

AB experience a force of attraction force PQ and RS.
Apply V = iR
` 200 i_1 xx 10 rArr i_1 = 20 A`
`200 = I_2 xx 20 rArr i_1 = 10 A`
AB will be in equilibrium if
`(mu_0)/( 2pia) i_2 i_3 l + mg = (mu_0 i_1 i_3)/(2 pi a)`
`(mu_0)/(2pi a) xx (i_1 i_3 - i_2i_3) l = mg `

`(4 pi xx 10^(-7))/(2 pi xx 5 xx 10^(-2))(20 i_3 -10 i_3) xx (1)/(100) =10^(-3) xx 9.8`
` (2 xx 10^(-5) xx 10 i_3)/(5) = 9.8 xx 10^(-3)`
`i_3 = 245A.`