A direct current `I` flows along a lengthly straight wire. From the point `O` (fig) the current sperads radially all over an infinite conducting plane paerpendicular to the wire. Find the magnatic induction at all points of space.

Explanation

It si easy to convince oneself that both in the regions. 1 and 2 there can be a circuilatal magnetic field (i.e., the component `B_(varphi))`. Any radilal field is region 1 or any `B_(Z)` away from the current plane will imply a violation of Gauss's law of magnetostaics, `B_(varphi)` must obviously be symmetrical about the straight wire. Then in 1,
`B_(varphi) 2pi r = mu_(0) I`
or, `B_(varphi) = (mu_(0))/(2pi) (I)/(r)`
In 2, `B_(varphi) 2pi r = 0`, or `B_(varphi) = 0`