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Asked by Prashant DIGHE | 02 Nov, 2019, 04:30: PM

Expert Answer

Magnetic field at a point P due to a current element idl is obtained from Biot-savart's law as given below

begin mathsize 12px style B with rightwards arrow on top space equals space fraction numerator mu subscript o over denominator 4 pi end fraction fraction numerator i stack d l with rightwards arrow on top space cross times space r with hat on top over denominator r squared end fraction space equals space fraction numerator mu subscript o over denominator 4 pi end fraction space fraction numerator i d l space sin theta over denominator r squared end fraction n with hat on top end style

where r is the ditance of current element from point P,

begin mathsize 14px style r with hat on top end style

is the unit vector along line joining current element and P

and

begin mathsize 14px style n with hat on top end style

is the unit vector perpendicular to both

begin mathsize 14px style i space stack d l with rightwards arrow on top end style

and

begin mathsize 14px style r with hat on top end style

. θ is angle between

begin mathsize 14px style i space stack d l with rightwards arrow on top end style

and

begin mathsize 14px style r with hat on top end style

Hence magnitude of magnetic field = 10^-7 × 10 × 2 × 10^-3 /(1 × 1) = 2×10^-9 T

as per the given diagram direction of magnetic field is in negative z-direction

(But the options are given in the question as if magnetic field is in (x,y) plane , that is not correct )

Answered by Thiyagarajan K | 02 Nov, 2019, 08:38: PM

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