A piece of copper is made into a rod with a square cross-section. The side of the square is 2.00 centimeters. The resistivity of copper is 1.7 \cdot 10^{-8} \Omega\cdot {\rm m}. An unknown electric field E, directed along the rod, creates a current of 12.0 amperes through the rod. Find the magnitude of E.

To find the magnitude of the electric field (E) created by the unknown electric field, you can use Ohm's Law, which is represented by the equation:

V = I * R

where V is the voltage, I is the current, and R is the resistance.

In this case, you are given the current (I) as 12.0 amperes, and you need to find the magnitude of the electric field (E), which can be related to the resistance (R) and the dimensions of the rod.

The resistance (R) can be calculated using the formula:

R = ρ * (L / A)

where ρ is the resistivity of copper (given as 1.7e-8 Ω·m), L is the length of the rod, and A is the cross-sectional area of the rod.

In this question, the cross-sectional area (A) is described as a square with a side length of 2.00 centimeters. To convert this to meters, you need to divide it by 100.

A = (2.00 cm)^2 / 100
A = 0.04 m^2

Now, you can rearrange the equation for resistance (R) to solve for the length of the rod (L):

R = ρ * (L / A)
L = R * A / ρ

Substituting the given values:

L = (12.0 Ω) * (0.04 m^2) / (1.7e-8 Ω·m)

Now, you have the length of the rod (L).

Finally, to find the magnitude of the electric field (E), you can use the equation:

E = V / L

In this case, since the voltage (V) is not given, you can assume it to be 1 volt. Therefore:

E = 1 V / L

Substituting the calculated value of L, you can find the magnitude of the electric field (E).