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Figure shows a rectangular current-carry...

Figure shows a rectangular current-carrying loop placed `2cm` away from a long, straight, current carrying conductor. What is the direction and magnitude of the net force acting on the loop?

Text Solution

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Here, `I_1=15A, I_2=25A`,
`r_1=2xx10^-2m, r_2=(2+10)xx10^-2m`
Force on BC, `F_1=(mu_0)/(4pi)(2I_1I_2)/(r_1)xxl enght BC`
`=10^-7xx(2xx15xx25)/((2xx10^-2))xx(25xx10^-2)`
`=9*375xx10^-4N` (repulsive, away from XY)
Force on DA, `F_2=(mu_0)/(4pi)(2I_1I_2)/(r_2)xx l eng th DA`
`=10^-7xx(2xx15xx25)/((2+10)xx10^-2)xx25xx10^-2`
`=1*5625xx10^-4N` (attractive towards XY)
Net force on the loop `F=F_1-F_2`
`=(9*375-1*5625)xx10^-4`
`=7*8175xx10^-4N`
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