Physics

Physics

Problem

A solenoid of 800 turns and length 0.50 m0.50\,\text{m} carries a current of 3.0 A3.0\,\text{A}. Take μ0=4π×10−7 H m−1\mu_0=4\pi\times10^{-7}\,\text{H m}^{-1}. The magnetic field inside the solenoid is closest to a) 6.0×10−4 T6.0\times10^{-4}\,\text{T} b) 3.0×10−3 T3.0\times10^{-3}\,\text{T} c) 6.0×10−3 T6.0\times10^{-3}\,\text{T} d) 3.0×10−4 T3.0\times10^{-4}\,\text{T}
Intuitive explanation

The magnetic field inside a solenoid depends on how tightly the coils are packed—specifically, the number of turns per unit length—and how much current flows through them. This is a straightforward application of the solenoid field formula B=μ0nIB = \mu_0 n I, where nn is the turn density. Just divide the total turns by the length to find how many coils exist per meter, then multiply by the current and the permeability constant.

Intuitive explanation

The magnetic field inside a solenoid depends on how tightly the coils are packed—specifically, the number of turns per unit length—and how much current flows through them. This is a straightforward application of the solenoid field formula B=μ0nIB = \mu_0 n I, where nn is the turn density. Just divide the total turns by the length to find how many coils exist per meter, then multiply by the current and the permeability constant.

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