A short circuit element vector dl = (.500mm) j hat carries a current of 9.2 A in

Question

A short circuit element vector dl = (.500mm) j hat carries a current of 9.2 A in the same direction as vector dl. Point P is located at vector r = (-.730m) i hat + (.390m) k hat. Find the magnetic field at P produced by this current element.

I know I need to use the Biot Savart equation and that the r hat equals vector r divided by r. I took the cross product of vector dl and vector r and got (1.95 x 10^-4 m^2) i hat + (.000365 m^2) k hat. I found the radius to be .8276m. I found dBx = 5.924 nanotelsas i hat, dBy = o nanotelsas and dBz equals -.3165 nanotelsas k hat but this is wrong. Thanks.

Explanation / Answer

B = (mu0/4*pi) * I *(dl x r_cap)/r^2

r_cap = -0.882 i + 0.471 k

dl x r = 0.5*10^-3 j x ( -0.882 i + 0.471 k)

         = 0.441*10^-3 k + 0.235*10^-3 i

r = 0.8276 m

B = 4*pi*10^-7/ (4*pi) * 9.2 * (0.441 k + 0.235 i )*10^-3 / 0.8276^2

= (5.924 k + 3.1565 i ) *10^-10

= (0.5924 k + 0.3157 i )nT

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