In an earlier section we learned that any increase in a current flowing in a loop causes an increase in the magnetic field produced by that current. Increasing flux gives rise to, or induces, a current with an emf that opposes the increase in the net magnetic field through the loop. The changing magnetic flux through the first loop does more than induce a current and magnetic field in the second loop: it also induces a current in the first loop itself, one that moves counter to the original current. Lenz's Law states that, as the magnetic flux changes in the second loop, the induced current creates a magnetic field that opposes change in the first field. This is known as self-induction. The emf in this case is called self-induced emf or back emf, and runs in the direction opposite that of the changing primary current. Grab the loop with your right hand. Your fingers point through the loop in the direction of the opposing magnetic field. Your thumb represents the current created by the opposing magnetic field. Notice that your thumb points opposite the direction of the primary current. Hence, the name back emf. We know from Faraday's Law that the induced emf equals the negative rate of change of the flux with time. The rate of change of flux with time is represented by the equation epsilon equals the negative derivative of phi with respect to time. Moreover, we know that magnetic field, B, equals mu zero, times the number of loops per unit length, times the current. Mu zero is a constant known as the permeability of free space. We can conclude from this expression that B is proportional to the current. These two proportionality relations imply that the flux is proportional to the current, and therefore the rate of change of flux is proportional to the change in current. From this relation we obtain a quantitative description of inductance. Inductance is the proportionality constant that links the rates of change of flux and current, and is equal to the number of loops times the flux divided by the current. We can also write the inductance as the ratio of the emf and the current rate. The SI unit for inductance is the Henry, represented by capital H, which equals 1 volt-second per ampere. Recalling that resistance equals emf divided by current, we can conclude that inductance is a form of resistance. Inductance creates a back emf, which opposes and reduces change in current. Suppose that you have a very long solenoid of length L, with N turns. Let's find its inductance. Let's start with the formula relating the magnetic field strength to the current and number of loops per length. The magnetic flux through each turn equals the magnetic field strength times the cross-sectional area times cosine theta. Since the angle between the magnetic field in the center of the solenoid and the area of each loop is zero degrees, the cosine factor can be left out. The magnetic flux equals, then, the magnetic field times the area. Substituting the expression for B into the magnetic flux equation gives flux in terms of current, area, and loops per length. Next we put this expression for flux into the inductance formula: n times flux squared divided by the current; which gives the final expression for inductance. Inductance equals mu zero times n squared times area divided by length. What is the value of inductance in a 10 centimeter long solenoid containing 355 loops each with an area of 0.250 squared centimeters? ... If this solenoid had an iron core with a magnetic permeability of five mu zero. What would be the inductance? ... Adding an iron core with a magnetic permeability of 5 mu would increase the inductance by a factor of five.

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