Magnetic Field due to a Wire, Loop, Solenoid

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In this lesson, we will discuss the induced magnetic field due to a wire, a loop, and a solenoid (coil of wires with many turns). Any wire with a current running through it induces a magnetic field. We can quantify the magnitude of the magnetic field due to a wire using the formula below.

\[B= \frac{\mu _0 I}{2πr}\]

Where:


And for a loop, we can quantify the magnetic field at its center using the formula

\[B= \frac{\mu _0 I}{2R}\]

Where R is the radius of the loop.


And finally, for an ideal solenoid at its center, the magnetic field can be quantified with the formula

\[B =\mu _0 nI\]

Where n is the number of turns per unit length of the solenoid.

A wire carries a current of 4A. What is the magnetic field 5 cm away from it?


Solution:

\(B= \frac{4π \times 10^{-7} \times 4}{2π \times 0.05} = 1.6 \times 10^{-5} \: \text{T}\)

What is the magnetic field at the center of a circular loop of radius 10 cm carrying a current of 3 A?


Solution:

\(B= \frac{4 \mu \times 10^{-7} \times 3}{2 \times 0.1} = 1.88 \times 10^{-5} \: \text{T}\)


Written by Mubarak Aouda