A long straight wire carries a current of `10A` directed along the negative y-axis as shown in A unifrom magnetic field `B_(0)` of magnetude `10^(-6) T` is directed parallel to the x-axis What is the resultant magnetic field at the following points
(a) `x =0,z =2m,` (b) `x =2m, z =0` (c) `x =0,z = - 0.5m`
.

Answer

(a) 0 (b) `1.41 xx 10^(-6) T, 45^(@)` in xzp-plane (c ) `5 xx 10^(6) T, + x`-direction .

Explanation

`oversetrarr(B)_((x=0,z=2))(mu_(0)) /(4pi
)(2I)/(r) (-hati) =10^(-7) xx (2 xx 10)/(2) (-hati)`
`oversetrarr(B)_(((x =0,z=2)))=10^(-6) (hati)T`
`oversetrarr(B) = oversetrarr(B_(0)) + oversetrarrB _((x =0,z=2) =0`
`oversetrarrB_(((x =2,z=0))) = (mu_(0))/(4pi) (2I)/(r) (+hatk) = 10^(-6) hatk (T)`
`oversetrarrB=oversetrarrB_(((x=2,z=0))) + oversetrarr(B_(0)) = 10^(-6)hatk + 10^(-6) hati`
`B = sqrt2 xx 10^(-6) T, 45^(@) "in x - z plane"`
`oversetrarrB_((x =0,z=-2)) = mu_(0)/(4pi) (I)/(r) (hati) = 4 xx 10^(-6) T`
` oversetrarrB =oversetrarrB_(((x=0,z=-2)))+oversetrarrB_(0)`
`oversetrarrB = 5 xx 10^(-6) (hati)` .