The Electromagnetic Door Lock · AI Generator #GEN-EBA6F92C

Physics · electromagnetism

Problem

A modern hotel uses electromagnetic door locks that operate on a simple principle: a solenoid creates a magnetic field that pulls a steel bolt into the locked position. The solenoid consists of N=800N = 800 turns of wire wound in a cylinder of length L=6.0  cmL = 6.0\;\text{cm} and cross-sectional area A=4.0  cm2A = 4.0\;\text{cm}^2. When a current of I=2.5  AI = 2.5\;\text{A} flows through the solenoid, it creates a uniform magnetic field inside. The steel bolt has a magnetic permeability μ=1200μ0\mu = 1200\mu_0, where μ0=4π×10−7  H/m\mu_0 = 4\pi \times 10^{-7}\;\text{H/m} is the permeability of free space. When the bolt is fully inserted into the solenoid, it completely fills the solenoid's interior. Calculate the magnetic energy stored in the solenoid when the steel bolt is locked in position and current is flowing.

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