Electrical Engineering Task_ I came to the solution indirectly, but I can't explain the formula to myself. It's only about a.)?

Task:

A consumer is connected to the grid with the effective value of the voltage U_{N} = 230 V via a 100 m long two-core copper cable with the specific resistance rho = 0.0178 Omega *mm² / m.

a) What is the maximum current density J that may occur if the voltage drop across the line is 2.5% of the mains voltage?

b) What is the minimum wire diameter d that must be selected if a maximum current of 10 A flows in the cable?

c) What is the line resistance R_{L}

d) By how many percent would the cable diameter have to be changed if the current is increased by 4%, but the current density is to remain constant?

Solution: a.) J= 1.62A/mm² b.) 2.81mm c.) RL= 0.57Omega d.) delta d= 2%

Solution for a.)

U_{perm} = 0.025 * U_{N} = 0.025 * 230 V = 5.75 V

These results in the maximum current density J:

J = U_{zul} / (rho * L) = 5.75 V / (0.0178 Omega*mm² * 200 m) = 1.62A/mm²

It is about this formula: J = U_{zul} / (rho * L)