Two infinitely long linear conductors are arranged perpendicular to each other and are in mutually perpendicular planes as shown in Fig. If `I_1=2A` along the y-axis, `I_2=3A`, along -ve z-axis and AP=AB=1cm, the value of magnetic field strength `vecB` at P is

Options

A. `(3xx10^-5T)hatj+(-4xx10^-5T) hatk`
B. `(3xx10^-5T)hatj+(4xx10^-5T) hatk`
C. `(4xx10^-5T)hatj+(-4xx10^-5T) hatk`
D. `(-3xx10^-5T)hatj+(4xx10^-5T) hatk`

Answer

B

Explanation

(b) Magnetic field strength at P due to `I_1`
`vecB_1=(mu_0I)/(2pi(AP))hatk=(4pixx10^-7xx2)/(2pixx1xx10^-2)hatk=(4xx10^-5T)hatk`
Magnetic field strength at P due the `I_2`
`vecB_2=(mu_0I_2)/(2pi(BP))hatj=(4pixx10^-7xx3)/(2pixx2xx10^-2)hatj=(3xx10^-5T)hatj`
Hence, `vecB=(3xx10^-5T)hatj+(4xx10^-5T)hatk`