Slide 1Fig 32-CO, p.1003

Slide 2  As the source current increases with time, the magnetic flux through the circuit loop due to this current also increases with time. This increasing flux creates an induced emf in the circuit.  The direction of the induced emf is such that it would cause an induced current in the loop (if a current were not already flowing in the loop), which would establish a magnetic field that would oppose the change in the source magnetic field.   - d  /dt

Slide 3 After the switch is closed, the current produces a magnetic flux through the area enclosed by the loop. As the current increases toward its equilibrium value, this magnetic flux changes in time and induces an emf in the loop.

Slide 4 For N turns coil where L is a proportionality constant—called the inductance of the coil From (1)

Slide 5Fig 32-2, p.1005 (a)A current in the coil produces a magnetic field directed to the left. (b)If the current increases, the increasing magnetic flux creates an induced emf having the polarity shown by the dashed battery. (c) The polarity of the induced emf reverses if the current decreases.

Slide 6p.1005 Inductance : a self-induced emf is always proportional to the time rate of change of the source current.

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Slide 10 Ex: A air core solenoid contains 500 turns with a length 40 cm and a cross sectional area 6 cm 2 Then the self-inductance is mH A 200 mH inductor carriers a steady current of 0.5 A. When the switch in the circuit is opened the current is effectively zero after 10 mS. What is the induced electromotive force emf in The inductor during this time 10 mV

Slide 11 RL circuit consists of battery are connected to a resistor and an inductor Suppose that the switch S is thrown closed at t =0. The current in the circuit begins to increase, and a back emf that opposes the increasing current is induced in the inductor. The back emf is we can apply Kirchhoff’s loop rule to this circuit, traversing the circuit in the clockwise direction

Slide 12 If we multiply each term by I and rearrange the expression, we have If we let U denote the energy stored in the inductor at any time, then we can write the rate dU/dt at which energy is stored as by apply Kirchhoff’s loop rule to this circuit, This expression indicates that the rate at which energy is supplied by the battery equals the sum of the rate at which energy is delivered to the resistor I 2 R,, and the rate at which energy is stored in the inductor,

Slide 13 We can also determine the energy density of a magnetic field. For simplicity, consider a solenoid whose inductance is given by The magnetic field of a solenoid is given by Equation

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Slide 15 Energy stored in a parallel-plate capacitor For a parallel-plate capacitor, the potential difference is related to the electric field through the relationship V = Ed.. The capacitance is given by By substituting The energy per unit volume known as the energy density, is The energy density in any electric field is proportional to the square of the magnitude of the electric field at a given point Ch 26

Slide 16 Ex: A long solenoid has a self inductance of 5  H. The energy stored in its magnetic filed when it carries a current of 10 A is : 250  J A long solenoid has a self inductance of 10  H. The energy stored in its magnetic filed when it carriers a current of 10 A is: 500  J Ex: If the magnetic filed is 15 mT, what is the magnetic energy density 89.57

Slide 17 The volume energy density In a space due to a magnetic filed of 0.5T equals: 100,000 The volume energy density stored in a magnetic filed B is proportional to:

Slide 18 If U E is the energy density resulted from an applied electric filed E And U B is the energy density from an applied magnetic filed B, then the ratio U E /U B will be The electric energy density

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