Calculate the electric field in a copper wire of cross-section area 2.0 mm2 carrying a current of 1 A. The resistivity of copper = 1.7 × 10–8 Ω m.
8.5mVm-1
Given,
Area of cross-section of wire, A=2.0 mm2=2×10-6 m2
Current flowing through the wire, I=1A
Resistivity of copper, ρ= 1.7 × 10–8 Ω m
Formula used,
From electrostatics, we know that Electric field, E is
Or it can be written as
Where l is the distance over which potential difference V has an effect
From Ohm’s law and the concept of current density, the relation connecting resistance, R and resistivity, ρ can be written as,
Where ‘l’ is the length of the conductor (or wire) and ‘A’ is the area of cross-section of the conductor.
Solution,
We know that potential difference, V is
Using eqn.2, the above expression can be modified as,
Now, in order to find the electric field by eqn.1, we can replace V in eqn.1 with the above expression as,
On simplification, it becomes,
We have all the values for the above expression. So, on substitution, Electric field will be,
Hence the electric field in a copper wire is 8.5mVm-1