Electromagnetic Fields and Waves: Notes, Solved Problems and Interactive Lab

Worked example 4.2.3

About the worked examples of Section 4.2

Three short calculations tied to the applications. They use only $L = Λ/ I$ , $W_{m} = \frac{1}{2} L I^{2}$ and the Lorentz force $F = \oint I d l \times B$ , and no new physics. Numerical constants: $μ_{0} = 4 π \times 1 0^{- 7} = 1.2566 \times 1 0^{- 6} H/m$ , $g = 9.81 m/ s^{2}$ . A good way to use them: read the given quantities, produce the formula from the corresponding application or problem yourself, and only then put the numbers in.

Worked example 4.2.3

Loudspeaker voice coil

cf. Application 4.2.3

Given. A loudspeaker gap with a radial field $B = 1.0 T$ . The voice coil has $N = 40$ turns of radius $a = 12 mm$ , all inside the gap, and carries $I = 1.5 A$ . The moving mass (coil, former and cone) is $m = 10 g$ .

Find. (a) the length of wire $l$ in the field and the force factor $B l$ , (b) the force on the coil, (c) the acceleration of the moving mass, in m/s $^{2}$ and in units of $g$ , (d) the force when the current reverses.

Try it yourself first.

Worked example 4.2.3: Loudspeaker voice coil