A stright segment `OC` (of length `L` meter) of a circuit carrying a current `2 amp` is placed along the `x`-axis.Two infinitely long straight wires `A` and `B` each extending form `z=oo`to`+oo`, are fixed at `y=-a metre` and `y=+a metre` respectively, as shown in the figure.If the wires `A` and `B` each carry a current `I` amp into plane of the paper.Obtain the expression for the force acting on the segment `OC`.The force on `OC` is `((mu_(0))/(N_(pi)))ln ((L^(2)+a^(2))/a^(2))(-hatk)`.Then find the value of `N`

Answer

0.5

Explanation

`B_(Net)=2B cos theta`
`=(2mu_(0)i)/(2pisqrt(a^(2)+x^(2)))x/sqrt(a^(2)+x^(2))`
`B_(Net)=(mu_(0)ix)/(pi(a^(2)+x^(2)))(-hatj)`
Magnetic force on differential element
`dF=(mu_(0)i^(2)x)/(x(a^(2)+b^(2))dx`
Net force `F=(mu_(0)i^(2))/(2pi)underset(0)overset(L)int(2x)/((a^(2)+x^(2)))dx=(mu_(0)i^(2))/(2pi) "In"((a^(2)+L^(2))/a^(2))`
direction along `(hatixx(-hatj))=-hatk`
On Reversing Current in `B`
Net field `=0`
Force `=0`