A long, straight wire, carrying a current 200A, runs through a cubical wooden box, entering and leaving through holes in the centre of opposite faces (as shown in Fig). The length of each side of the box is 20 cm. Consider an element `dl,0.100 cm` long of the wire at the centre of the box. Compute the magnitude dB of the magnetic field produced by this element at the point a, b,c,d and e as shown fig. Points a,c, and dare at the centres of the faces of the cube, point b is at the midpoint of one edge, and point e is at a corner. Copy the figure and show the direction and relative magnitudes of field vectors.

Explanation

The magnetic fields at the given point are
`dB_a=(mu_0)/(4pi) (Idl sin theta)/(r^2)=(mu_0)/(4pi) ((200A)(0.00100m))/((0.10m)^2)`
`=2.00xx10^-6T`
`dB_b=(mu_0)/(4pi) (Idl sin theta)/(r^2)=(mu_0)/(4pi) ((200A)(0.00100m)sin 45^@)/((sqrt2xx0.10m)^2)`
`=0.707xx10^-6T`
`dB_c=(mu_0)/(4pi) (Idl sin theta)/(r^2)=(mu_0)/(4pi) ((200A)(0.00100m))/((0.10m)^2)`
`=2.00xx10^-6T`
`dB_d=(mu_0)/(4pi) (Idl sin theta)/(r^2)=(mu_0)/(4pi) (Idl sin(0^@))/(r^2)=0`
`dB_e=(mu_0)/(4pi) (Idl sin theta)/(r^2)=(mu_0)/(4pi) ((200A)(0.00100m))/((sqrt3xx0.100m)^2) (sqrt2)/(sqrt3)`
`=5.45xx10^-6T`