A wire is connected to batteries $($not shown$),$ and current flows through the wire. The wire lies flat on a table, and you are looking down on it from above. The wire is laid on top of a compass, resting about $4$ mm above the needle. The distance $\backslash ($ d $\backslash )$ is $6\mathrm{.}5$ cm $.$ The compass needle deflects $18$ degrees from North, as shown. At this location the horizontal component of the Earth's magnetic field is $\backslash (2\backslash$mathrm$\{$e$\}-5\backslash )$ tesla.

What is the direction of the magnetic field at location $\backslash ($ A $\backslash ),$ midway between the wires, due to the current in the wire?

What is the approximate magnitude of the magnetic field at location $\backslash ($ A $\backslash ),$ due to the current in the wire?

$\backslash (|\backslash$vec$\{$B$\}|=\backslash )$

What approximations or assumptions did you make in solving this problem?

Assume the bent end of the wire is far from location $\backslash ($ A $\backslash )$

Assume that at the location of the compass the effect of the distant wire is negligible

Assume the Earth's magnetic field is negligible

Assume one side of the wire is much longer than $\backslash ($ d $\backslash )$