A Nichrome wire 25 cm long and 0.22 mm in diameter is connected to a 2.3 V flashlight battery.
(A) What is the electric field inside the wire?
(B) Why don't you have to know how the wire is bent? (Select all that apply.)

a. E is dependent on the length L of the wire which only applies to the segment of the wire that is not bent.
b. E is not dependent on how the wire is bent, only the diameter of the wire is needed.
c. Since the conventional current flows in the direction of E → , E is the same in every part of the wire with uniform properties.
d. E must be parallel to the wire at every location – even if the wire twists and turns.

(A) E = 9.2V/m

(a) and (d)

Explanation:

E = V/L

Given V = 2.3 V and L = 25cm = 0.25m

E = 2.3/0.25 = 9.2 V/m.

The electric field is constant and uniform throughout the length of the wire. Mathematically,

E = dV/dr

E is the ratio of a very small potential difference across a very small section of a conductor. It is the constant of proportionality between the potential difference applied across the ends of the wire. The potential difference varies over the length of the wire having a high value at the positive terminal and reduces to zero over the length of the wire to the negative terminal. As a result E is always the same at every point in the wire provided the wire has uniform properties.

Also from this equation E = dV/dr it can be seen that the magnitude of E is the slope of the tangent to the curve formed by varying V and dr. The direction is always tangent to the wire. In other words just like in statement (d) the E is always parallel to the wire even if it is curved.