A solenoid of length 4.00 cm and cross-sectional area 2.00 cm² has 80 turns.What is its self-inductance? A) 160 $\mu$H B) 120 $\mu$H C) 80.0 $\mu$H D) 40.0$\mu$H E) 0.500 $\mu$H

Question

Quizplus · Accepted Answer

The formula for the self-inductance of a solenoid is:

L = μ₀n²Aℓ

Where:
μ₀ = 4π × 10⁻⁷ H/m
n = number of turns per unit length
A = cross-sectional area
ℓ = length

Plugging in the given values:

n = 80/0.04 = 2000 turns/m
A = 2.00 cm² = 2.00 × 10⁻⁴ m²
ℓ = 0.04 m

L = (4π × 10⁻⁷ H/m) × (2000 turns/m)² × (2.00 × 10⁻⁴ m²) × 0.04 m
L = 40.0 μH = 40.0 × 10⁻⁶ H = 40.0 mH = 0.04 H

Therefore, the self-inductance of the solenoid is 40.0 μH or 0.04 H. The closest answer choice is D) 40.0 μH or 40.0 × 10⁻⁶ H.

A Solenoid of Length 4 μ\muμ H B) 120 μ\muμ H C) 80

A Solenoid of Length 4 $\mu$ H
B) 120 $\mu$ H
C) 80