Shortening or compressing the coil causes an increase in inductance.The addition of a core material to a solenoid can greatly affect its inductance. A core is sometimes added to a solenoid for any of a number of reasons, and the addition of a core material can affect inductance in either direction, depending on a property called permeability, which is a measure of how well a material distributes electric current. It can be shown that the This expression is similar to that for the energy stored in a capacitor.How much energy is stored in the 0.632 mH inductor of the preceding example when a 30.0 A current flows through it?The energy is given by the equation \(E_{ind} = \frac{1}{2}LI^2\), and all quantities except \(E_{ind}\) are known.Substituting the value for \(L\) found in the previous example and the given current into \(E_{ind} = \frac{1}{2}LI^2\) gives\[0.5(0.632 \times 10^{-3} \, H)(30.0 \, A)^2 = 0.284 \, J.\]This amount of energy is certainly enough to cause a spark if the current is suddenly switched off.
We express this in equation form as\[emf_2 = - M\dfrac{\Delta I_1}{\Delta t},\] where \(M\) is defined to be the mutual inductance between the two devices. We start by noting that the induced emf is given by Faraday’s law of induction as \(emf = -N(\Delta \Phi /\Delta t)\) and, by the definition of self-inductance, as \(emf = -L(\Delta I/\Delta t)\). (Here \(n = N/l\), where \(N\) is the number of coils and \[L = N\dfrac{\Delta \Phi}{\Delta I} = N \dfrac{\mu_0 NA \frac{\Delta I}{l}}{\Delta I}.\]This simplifies to \[L = \dfrac{\mu_0 N^2 A}{l} (solenoid).\]This is the self-inductance of a solenoid of cross-sectional area \(A\) and length \(l\). Objective Determine the inductance of various solenoids. (But they will not be able to detect any plastic explosive such as that found on the “underwear bomber.”) See We know from Lenz’s law that inductances oppose changes in current. Units of self-inductance are henries (H) just as for mutual inductance.
Example \(\PageIndex{1}\): Calculating the Self-inductance of a Moderate Size Solenoid. The body of the car increases the inductance and the circuit changes sending a signal to the traffic lights to change colors. This is the self-inductance of a solenoid of cross-sectional area \(A\) and length \(l\). The addition of a core material to a solenoid can greatly affect its inductance. The pulsed signal in the transmitter coil induces a signal in the receiver. One exception is the solenoid, because it has a very uniform field inside, a nearly zero field outside, and a simple shape. The inductance can be calculated in a manner similar to that for any coil of wire. Toroidal radius r = cm with N = turns, Coil radius = cm gives area A = cm 2. This is expressed as the area of the cross section of the solenoid. To avoid this effect, a smal \(L\) must be achieved, such as by counterwinding coils as in A 1 H inductor is a large inductor. A core is sometimes added to a solenoid for any of a number of reasons, and the addition …
To find \(\Delta B\), we note that the magnetic field of a solenoid is given by \(B = \mu_0 n I = \mu_0 \frac{\Delta I}{l}\).
The size and shape of the solenoid are the primary factors which affect inductance, but the material is also a consideration. (Remember that we need a changing magnetic field, brought about by a changing current, to induce a voltage in another coil.)
For example, the coils in Nature is symmetric here.
Its inductance of nearly a millihenry is also considered moderate.One common application of inductance is used in traffic lights that can tell when vehicles are waiting at the intersection. Substituting these into the expression for \(L\) gives\[L = \dfrac{(4\pi \times 10^{-7} \, T \cdot m/A)(200)^2(1.26 \times 10^{-3} \, m^2)}{0.100 \, m}\]This solenoid is moderate in size.
Inductance is calculated by means of fairly complex equations, but the factors which affect it are fairly easy to understand and have to do with the physical properties of the solenoid and how the wire is wound. Transformers, for example, are designed to be particularly effective at inducing a desired voltage and current with very little loss of energy to other forms. What is the mutual inductance of the two solenoids?
The larger the mutual inductance \(M\), the more effective the coupling. Since the area \(A\) of a solenoid is fixed, the change in flux is \(\Delta \Phi = \Delta (BA) = A\Delta B\). Shortening or compressing the coil causes an increase in inductance. Such large emfs can cause arcs, damaging switching equipment, and so it may be necessary to change current more slowly.There are uses for such a large induced voltage. Equating these yields\[emf = -N\dfrac{\Delta \Phi}{\Delta t} = -L \dfrac{\Delta I}{\Delta t}.\]Solving for \(L\) gives \[L = N\dfrac{\Delta \Phi}{\Delta I}.\]This equation for the self-inductance \(L\) of a device is always valid. All other factors remaining unchanged, lengthening or stretching the coil reduces inductance.
Glossary henry (H) unit of inductance, ; it is also expressed as a volt second per ampere inductance property of a device that tells how effectively it induces an emf in another device mutual inductance geometric quantity that expresses how effective two devices are at inducing emfs in one another . That is to say, each is examined as a separate case for how they affect inductance. Clear answers for common questions We want to hear from you.Induction is the process in which an emf is induced by changing magnetic flux. 02. If the coil is assumed to be a cylinder, it is the area of the circle forming either end of the cylinder. We want a transformer to have a large mutual inductance. What happens if we try to shut off the current rapidly, perhaps in only 1.0 ms? (10 = 414 X 10-7 T. M/A) 13) A) 4.19 PH B) 4.19 H C) 4.19 MH D) 4.19 NH E) 4.19 UH.
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