Question

Write an expression for the characteristic time τ of the solenoid in terms of the wire diameter d, the number of turns n, the solenoid diameter d, and the resistivity rho of copper (rho=1.68×10-8Ω ⋅ m)?

Answer 1

The characteristic time (τ) of a solenoid can be calculated using the formula τ = (π * D² * n² * ρ) / (4 * d²), where D is the solenoid diameter, n is the number of turns, d is the wire diameter, and ρ is the resistivity of copper.

Step-by-step explanation:

The characteristic time (τ) of a solenoid can be expressed in terms of the wire diameter (d), number of turns (n), solenoid diameter (D), and resistivity (ρ) of copper. The equation for the characteristic time is:

τ = (π * D² * n² * ρ) / (4 * d²)

For example, if the wire diameter is 0.2 cm, number of turns is 100, solenoid diameter is 5 cm, and resistivity of copper is 1.68 × 10^-8 Ω · m, the characteristic time can be calculated using the above formula.