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A current element 3dl is at (0,0,0) alon...

A current element `3dl` is at `(0,0,0)` along y-axis. If `dl=1cm`, find the magnetic field at a distance `20cm` on the x-axis.

Text Solution

Verified by Experts

Here, `dl=1cm=10^-2cm`,
`r=(20cm)=(0.20cm)` and `vecr=0.2hati`
`Idvecl=(3xx10^-2)hatj`
`dvecB=(mu_0)/(4pi)(Idveclxxvecr)/(r^3)`
`=(10^7xx(3xx10^-2hatj)xx(0.20hatj))/((0.20)^3)`
`=7*5xx10^-8(hatjxxhati)=7*5xx10^-8(-hatk)`
`=-(7.5xx10^-8T)hatk`
Thus magnitude of magnetic field is `7.5xx10^-8T` and its direction is along negative z-axis.
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