Problem $2$: $(9\%$ of Assignment Value$)$

Consider a wire carrying a current due east in a location where the Earth's field is due north.

Part $($a$)$

What is the direction of the force on the wire if both are parallel to the ground?

Down into the ground North East

West Up from the ground. None of these.

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Part $($b$)$

Calculate the force per unit length on the wire, in newtons per meter, if the wire carries $18$ A and the field strength is $3\mathrm{.}2{10}^{-5}T$ :

Part $($c$)$

What would the diameter be$,$ in meters, of copper wire $($with density $=8\mathrm{.}80{10}^{3}k\frac{g}{m^3})$ that would have its weight supported by this force in meters?

Part $($d$)$

Calculate the resistance per unit length, in ohms per meter, that this copper wire will have. Copper has a resistivity of ${}_R=1\mathrm{.}72{10}^{-8}*m.$

Part $($e$)$

Calculate the potential difference per unit length, in volts per meter, of this wire.