A straight segment `OC` (of lengh `L`) of a circuit carrying a current I is placed along the x-axis. Two infinitely long straight wire `A` and `B` each extending from `z=-ooto+oo` are fixed at `y=-a` and `y=+a` respectively as show in the figure. If the wires `A` and `B` each carry a current I into the plane of the paper, obtain the expression for the force acting on the segment `OC`. What will be the force on `OC` if the current in the wire `B` is reversed?

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`