Chapter 23 Magnetic Flux and Faraday’s Law of Induction
Units of Chapter 23 Induced Electromotive Force Magnetic Flux Faraday’s Law of Induction Lenz’s Law Mechanical Work and Electrical Energy Generators and Motors
Units of Chapter 23 Inductance RL Circuits Energy Stored in a Magnetic Field Transformers
23-1 Induced Electromotive Force Faraday’s experiment: closing the switch in the primary circuit induces a current in the secondary circuit, but only while the current in the primary circuit is changing.
23-1 Induced Electromotive Force The current in the secondary circuit is zero as long as the current in the primary circuit, and therefore the magnetic field in the iron bar, is not changing. Current flows in the secondary circuit while the current in the primary is changing. It flows in opposite directions depending on whether the magnetic field is increasing or decreasing. The magnitude of the induced current is proportional to the rate at which the magnetic field is changing.
23-1 Induced Electromotive Force Note the motion of the magnet in each image:
23-2 Magnetic Flux Magnetic flux is used in the calculation of the induced emf.
23-3 Faraday’s Law of Induction Faraday’s law: An emf is induced only when the magnetic flux through a loop changes with time.
23-3 Faraday’s Law of Induction There are many devices that operate on the basis of Faraday’s law. An electric guitar pickup:
23-4 Lenz’s Law Lenz’s Law An induced current always flows in a direction that opposes the change that caused it. Therefore, if the magnetic field is increasing, the magnetic field created by the induced current will be in the opposite direction; if decreasing, it will be in the same direction.
23-4 Lenz’s Law This conducting rod completes the circuit. As it falls, the magnetic flux decreases, and a current is induced.
23-4 Lenz’s Law The force due to the induced current is upward, slowing the fall.
23-4 Lenz’s Law Currents can also flow in bulk conductors. These induced currents, called eddy currents, can be powerful brakes.
23-5 Mechanical Work and Electrical Energy This diagram shows the variables we need to calculate the induced emf.
23-5 Mechanical Work and Electrical Energy Change in flux: Induced emf: Electric field caused by the motion of the rod:
23-5 Mechanical Work and Electrical Energy If the rod is to move at a constant speed, an external force must be exerted on it. This force should have equal magnitude and opposite direction to the magnetic force:
23-5 Mechanical Work and Electrical Energy The mechanical power delivered by the external force is: Compare this to the electrical power in the light bulb: Therefore, mechanical power has been converted directly into electrical power.
23-6 Generators and Motors An electric generator converts mechanical energy into electric energy: An outside source of energy is used to turn the coil, thereby generating electricity.
23-6 Generators and Motors The induced emf in a rotating coil varies sinusoidally:
23-6 Generators and Motors An electric motor is exactly the opposite of a generator – it uses the torque on a current loop to create mechanical energy.
23-7 Inductance When the switch is closed in this circuit, a current is established that increases with time.
23-7 Inductance Inductance is the proportionality constant that tells us how much emf will be induced for a given rate of change in current: Solving for L,
23-7 Inductance Given the definition of inductance, the inductance of a solenoid can be calculated: When used in a circuit, such a solenoid (or other coil) is called an inductor.
23-8 RL Circuits When the switch is closed, the current immediately starts to increase. The back emf in the inductor is large, as the current is changing rapidly. As time goes on, the current increases more slowly, and the potential difference across the inductor decreases.
23-8 RL Circuits This shows the current in an RL circuit as a function of time. The time constant is:
23-9 Energy Stored in a Magnetic Field It takes energy to establish a current in an inductor; this energy is stored in the inductor’s magnetic field. Considering the emf needed to establish a particular current, and the power involved, we find:
23-9 Energy Stored in a Magnetic Field We know the inductance of a solenoid; therefore, the magnetic energy stored in a solenoid is: Dividing by the volume to find the energy density gives: This result is valid for any magnetic field, regardless of source.
23-10 Transformers A transformer is used to change voltage in an alternating current from one value to another.
23-10 Transformers By applying Faraday’s law of induction to both coils, we find: Here, p stands for the primary coil and s the secondary.
23-10 Transformers The power in both circuits must be the same; therefore, if the voltage is lower, the current must be higher.
Summary of Chapter 23 A changing magnetic field can induce a current in a circuit. The magnitude of the induced current depends on the rate of change of the magnetic field. Magnetic flux: Faraday’s law gives the induced emf:
Summary of Chapter 23 Lenz’s law: an induced current flows in the direction that opposes the change that created the current. Motional emf: emf produced by a generator: An electric motor is basically a generator operated in reverse. Inductance occurs when a coil with a changing current induces an emf in itself.
Summary of Chapter 23 Definition of inductance: Inductance of a solenoid: An RL circuit has a characteristic time constant:
Summary of Chapter 23 Current in an RL circuit after closing the switch: Magnetic energy density: Transformer equation: