Question

At room temperature what is the strength of the electric field in a 12-gauge copper wire (diameter 2.05 mm that is needed to cause a 2.75 a current to flow?

Answer 1

Electric field strength = resistivity of copper x current density
where
p= 1.72 x 10^-8 ohm meter
diameter = 2.05mm=.00205 m
current = 2.75 A
get first the current density:
current density = current/ cross section area
find the cross section area
cross section area = pi.(d/2)^2;  
cross section = 3.3 006x10-6 m^2
substitute the values 
current density = 2.75A/3.3006x 10-6m^2
current density=35.55 x1 0^2 A/m^2
Electric field stregnth =1.72 x 10^-8 ohm meter x 35.55 x10^2 A/m^2
Electric field stregnth= 46.415 Volts/m

The electric field strength of copper is 46.415 V/m.